Sub-nyquist complex-holographic aperture antenna configured to define selectable, arbitrary complex electromagnetic fields

ABSTRACT

Described embodiments include an antenna, method, and an apparatus. The antenna includes a sub-Nyquist complex-holographic aperture configured to define at least two selectable, arbitrary complex radiofrequency electromagnetic fields on a surface with tangential wavenumbers up to 2π over the aperture element spacing (k_apt=2π/a).

If an Application Data Sheet (ADS) has been filed on the filing date ofthis application, it is incorporated by reference herein. Anyapplications claimed on the ADS for priority under 35 U.S.C. §§119, 120,121, or 365(c), and any and all parent, grandparent, great-grandparent,etc. applications of such applications, are also incorporated byreference, including any priority claims made in those applications andany material incorporated by reference, to the extent such subjectmatter is not inconsistent herewith.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of the earliest availableeffective filing date(s) from the following listed application(s) (the“Priority Applications”), if any, listed below (e.g., claims earliestavailable priority dates for other than provisional patent applicationsor claims benefits under 35 USC §119(e) for provisional patentapplications, for any and all parent, grandparent, great-grandparent,etc. applications of the Priority Application(s)).

PRIORITY APPLICATIONS

The present application claims benefit of priority of U.S. ProvisionalPatent Application No. 61/917,254, entitled METHODS AND DEVICES FORWIRELESS POWER BEAMING, naming Tom Driscoll, David R. Smith and YaroslavA. Urzhumov as inventors, filed 17 Dec. 2013, which was filed within thetwelve months preceding the filing date of the present application or isan application of which a currently co-pending priority application isentitled to the benefit of the filing date.

If the listings of applications provided above are inconsistent with thelistings provided via an ADS, it is the intent of the Applicant to claimpriority to each application that appears in the DomesticBenefit/National Stage Information section of the ADS and to eachapplication that appears in the Priority Applications section of thisapplication.

All subject matter of the Priority Applications and of any and allapplications related to the Priority Applications by priority claims(directly or indirectly), including any priority claims made and subjectmatter incorporated by reference therein as of the filing date of theinstant application, is incorporated herein by reference to the extentsuch subject matter is not inconsistent herewith.

SUMMARY

For example, and without limitation, an embodiment of the subject matterdescribed herein includes an apparatus. The apparatus includes asub-Nyquist complex-holographic aperture configured to define at leasttwo selectable, arbitrary complex radiofrequency electromagnetic fieldson a surface with tangential wavenumbers up to 2π over the apertureelement spacing (k_apt=2π/a).

In an embodiment, the sub-Nyquist complex-holographic aperture includesa plurality of individual electromagnetic wave scattering elementsdistributed on the surface. Each electromagnetic wave scattering elementhaving a respective electronically controllable electromagnetic responseto an incident radiofrequency electromagnetic wave. The plurality ofindividual electromagnetic wave scattering elements are electronicallycontrollable in combination to define the at least two selectable,arbitrary complex radiofrequency electromagnetic fields on the surface.

For example, and without limitation, an embodiment of the subject matterdescribed herein includes a method. The method includes receiving anincident radiofrequency electromagnetic wave. The method includesdefining a selected arbitrary complex radiofrequency electromagneticfield on a surface using a sub-Nyquist complex-holographic apertureconfigured to define at least two selectable, arbitrary complexradiofrequency electromagnetic fields on the surface with tangentialwavenumbers up to 2π over the aperture element spacing (k_apt=2π/a). Thearbitrary complex radiofrequency electromagnetic field selected from atleast two selectable, arbitrary complex radiofrequency electromagneticfields. The method includes transmitting radiofrequency electromagneticwaves coherently reconstructed from the incident radiofrequencyelectromagnetic waves by the selected arbitrary complex radiofrequencyelectromagnetic field defined on the surface.

In an embodiment, the method includes defining another selectedarbitrary complex radiofrequency electromagnetic field on the surfaceusing the sub-Nyquist complex-holographic aperture. The other arbitrarycomplex radiofrequency electromagnetic field is selected from the atleast two selectable, arbitrary complex radiofrequency electromagneticfields. This embodiment also includes transmitting additionalradiofrequency electromagnetic waves coherently reconstructed from theincident radiofrequency electromagnetic waves by the other selectedarbitrary complex radiofrequency electromagnetic field defined on thesurface.

For example, and without limitation, an embodiment of the subject matterdescribed herein includes an apparatus. The apparatus includes a meansfor receiving incident radiofrequency electromagnetic waves. Theapparatus includes means for defining a selected arbitrary complexradiofrequency electromagnetic field on a surface with tangentialwavenumbers up to 2π over the aperture element spacing (k_apt=2π/a), thearbitrary complex radiofrequency electromagnetic field selected from atleast two selectable, arbitrary complex radiofrequency electromagneticfields. The apparatus includes means for transmitting radiofrequencyelectromagnetic waves coherently reconstructed from the incidentradiofrequency electromagnetic waves by the selected arbitrary complexradiofrequency electromagnetic field defined on the surface. In anembodiment, the apparatus includes means for selecting the arbitrarycomplex radiofrequency electromagnetic field from the at least twoselectable, arbitrary complex radiofrequency electromagnetic fields.

For example, and without limitation, an embodiment of the subject matterdescribed herein includes a method. The method includes receivingradiofrequency electromagnetic waves at a first surface of a generallyplanar structure having the first surface and a second surface. Themethod includes defining a selected arbitrary complex radiofrequencyelectromagnetic field on the second surface using a sub-Nyquistcomplex-holographic aperture configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields onthe second surface with tangential wavenumbers up to 2π over theaperture spacing (k_apt=2π/a). The arbitrary complex radiofrequencyelectromagnetic field is selected from at least two selectable,arbitrary complex radiofrequency electromagnetic fields. The methodincludes transmitting from the second surface radiofrequencyelectromagnetic waves coherently reconstructed from the receivedradiofrequency electromagnetic waves by the selected arbitrary complexradiofrequency electromagnetic field defined on the second surface. Inan embodiment, the method includes selecting the arbitrary complexradiofrequency electromagnetic field from the at least two selectable,arbitrary complex radiofrequency electromagnetic fields.

The foregoing summary is illustrative only and is not intended to be inany way limiting. In addition to the illustrative aspects, embodiments,and features described above, further aspects, embodiments, and featureswill become apparent by reference to the drawings and the followingdetailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example embodiment of an environment 1719 thatincludes a thin computing device 1720 in which embodiments may beimplemented;

FIG. 2 illustrates an example embodiment of an environment 1800 thatincludes a general-purpose computing system 1810 in which embodimentsmay be implemented;

FIG. 3 illustrates an environment 1900 in which embodiments may beimplemented;

FIG. 4 illustrates an alternative embodiment of the antenna 1910;

FIG. 5 illustrates an alternative embodiment 2000 of the antenna 1910;

FIG. 6 illustrates an embodiment 2100 of the antenna 1910;

FIG. 7 illustrates an example operational flow 2200;

FIG. 8 illustrates an example apparatus 2300;

FIG. 9 illustrates an example operational flow 2400;

FIG. 10 illustrates an example apparatus 2500;

FIG. 11 illustrates an example environment 2600 that includes an antenna2610;

FIG. 12 illustrates an alternative embodiment of the environment 2700that includes an antenna 2710;

FIG. 13 illustrates an example operational flow 2800;

FIG. 14 illustrates an example apparatus 2900;

FIG. 15 includes an example operational flow 3000;

FIG. 16 illustrates certain aspects of an environment 3100, and a system3105;

FIG. 17 illustrates an embodiment of the associated system apparatus3150 described in conjunction with FIG. 16;

FIG. 18 illustrates an alternative embodiment 3102A of the radiateablespace 3102 of FIG. 16;

FIG. 19 illustrates an alternative embodiment 3102B of the radiateablespace 3102 of FIG. 16;

FIG. 20 illustrates alternative embodiments 3110A and 3110 B of theantenna 3110 illustrated in conjunction with FIGS. 18-19;

FIG. 21 illustrates an example operational flow 3200;

FIG. 22 illustrates an example apparatus 3300;

FIG. 23 illustrates certain aspects of an environment 3400;

FIG. 24 illustrates an embodiment of the associated system apparatus3450;

FIG. 25 illustrates an example operational flow 3500; and

FIG. 26 illustrates an example apparatus 3600.

DETAILED DESCRIPTION

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 12/286,740, entitled BEAM POWER FORLOCAL RECEIVERS, naming Roderick A. Hyde et al. as inventors, filed onSep. 30, 2008, is related to the present application. That applicationis incorporated by reference herein, including any subject matterincluded by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 12/286,737, entitled BEAM POWER WITHMULTIPOINT BROADCAST, naming Roderick A. Hyde et al. as inventors, filedon Sep. 30, 2008, is related to the present application. Thatapplication is incorporated by reference herein, including any subjectmatter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 12/286,755, entitled BEAM POWER WITHMULTIPOINT RECEPTION, naming Roderick A. Hyde et al. as inventors, filedon Sep. 30, 2008, is related to the present application. Thatapplication is incorporated by reference herein, including any subjectmatter included by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 12/286,741, entitled BEAM POWER WITHBEAM REDIRECTION, naming Roderick A. Hyde et al. as inventors, filed onSep. 30, 2008, is related to the present application. That applicationis incorporated by reference herein, including any subject matterincluded by reference in that application.

This application makes reference to technologies described more fully inU.S. Patent Application No. 61/455,171, entitled SURFACE SCATTERINGANTENNAS, naming Nathan Kundtz as inventor, filed Oct. 15, 2010, isrelated to the present application. That application is incorporated byreference herein, including any subject matter included by reference inthat application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 13/317,338, entitled SURFACE SCATTERINGANTENNAS, naming Adam Bily et al. as inventors, filed Oct. 14, 2011, isrelated to the present application. That application is incorporated byreference herein, including any subject matter included by reference inthat application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 13/838,934, entitled SURFACE SCATTERINGANTENNA IMPROVEMENTS, naming Adam Bily et al. as inventors, filed Mar.15, 2013, is related to the present application. That application isincorporated by reference herein, including any subject matter includedby reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/102,253, entitled SURFACE SCATTERINGREFLECTOR ANTENNA, naming Jeffrey A. Bowers et al. as inventors, filedDec. 10, 2013, is related to the present application. That applicationis incorporated by reference herein, including any subject matterincluded by reference in that application.

This application makes reference to technologies described more fully inU.S. patent application Ser. No. 14/226,213, entitled SURFACE SCATTERINGANTENNA ARRAY, naming Jesse R. Cheatham, III et al. as inventors, filedMar. 26, 2014, is related to the present application. That applicationis incorporated by reference herein, including any subject matterincluded by reference in that application.

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative embodiments described in thedetailed description, drawings, and claims are not meant to be limiting.Other embodiments may be utilized, and other changes may be made,without departing from the spirit or scope of the subject matterpresented here.

FIGS. 1 and 2 provide respective general descriptions of severalenvironments in which implementations may be implemented. FIG. 1 isgenerally directed toward a thin computing environment 1719 having athin computing device 1720, and FIG. 2 is generally directed toward ageneral purpose computing environment 1800 having general purposecomputing device 1810. However, as prices of computer components dropand as capacity and speeds increase, there is not always a bright linebetween a thin computing device and a general purpose computing device.Further, there is a continuous stream of new ideas and applications forenvironments benefited by use of computing power. As a result, nothingshould be construed to limit disclosed subject matter herein to aspecific computing environment unless limited by express language.

FIG. 1 and the following discussion are intended to provide a brief,general description of a thin computing environment 1719 in whichembodiments may be implemented. FIG. 1 illustrates an example systemthat includes a thin computing device 1720, which may be included orembedded in an electronic device that also includes a device functionalelement 1750. For example, the electronic device may include any itemhaving electrical or electronic components playing a role in afunctionality of the item, such as for example, a refrigerator, a car, adigital image acquisition device, a camera, a cable modem, a printer anultrasound device, an x-ray machine, a non-invasive imaging device, oran airplane. For example, the electronic device may include any itemthat interfaces with or controls a functional element of the item. Inanother example, the thin computing device may be included in animplantable medical apparatus or device. In a further example, the thincomputing device may be operable to communicate with an implantable orimplanted medical apparatus. For example, a thin computing device mayinclude a computing device having limited resources or limitedprocessing capability, such as a limited resource computing device, awireless communication device, a mobile wireless communication device, asmart phone, an electronic pen, a handheld electronic writing device, ascanner, a cell phone, a smart phone (such as an Android® or iPhone®based device), a tablet device (such as an iPad®) or a Blackberry®device. For example, a thin computing device may include a thin clientdevice or a mobile thin client device, such as a smart phone, tablet,notebook, or desktop hardware configured to function in a virtualizedenvironment.

The thin computing device 1720 includes a processing unit 1721, a systemmemory 1722, and a system bus 1723 that couples various systemcomponents including the system memory 1722 to the processing unit 1721.The system bus 1723 may be any of several types of bus structuresincluding a memory bus or memory controller, a peripheral bus, and alocal bus using any of a variety of bus architectures. The system memoryincludes read-only memory (ROM) 1724 and random access memory (RAM)1725. A basic input/output system (BIOS) 1726, containing the basicroutines that help to transfer information between sub-components withinthe thin computing device 1720, such as during start-up, is stored inthe ROM 1724. A number of program modules may be stored in the ROM 1724or RAM 1725, including an operating system 1728, one or more applicationprograms 1729, other program modules 1730 and program data 1731.

A user may enter commands and information into the computing device 1720through one or more input interfaces. An input interface may include atouch-sensitive screen or display surface, or one or more switches orbuttons with suitable input detection circuitry. A touch-sensitivescreen or display surface is illustrated as a touch-sensitive display1732 and screen input detector 1733. One or more switches or buttons areillustrated as hardware buttons 1744 connected to the system via ahardware button interface 1745. The output circuitry of thetouch-sensitive display 1732 is connected to the system bus 1723 via avideo driver 1737. Other input devices may include a microphone 1734connected through a suitable audio interface 1735, or a physicalhardware keyboard (not shown). Output devices may include the display1732, or a projector display 1736.

In addition to the display 1732, the computing device 1720 may includeother peripheral output devices, such as at least one speaker 1738.Other external input or output devices 1739, such as a joystick, gamepad, satellite dish, scanner or the like may be connected to theprocessing unit 1721 through a USB port 1740 and USB port interface1741, to the system bus 1723. Alternatively, the other external inputand output devices 1739 may be connected by other interfaces, such as aparallel port, game port or other port. The computing device 1720 mayfurther include or be capable of connecting to a flash card memory (notshown) through an appropriate connection port (not shown). The computingdevice 1720 may further include or be capable of connecting with anetwork through a network port 1742 and network interface 1743, andthrough wireless port 1746 and corresponding wireless interface 1747 maybe provided to facilitate communication with other peripheral devices,including other computers, printers, and so on (not shown). It will beappreciated that the various components and connections shown areexamples and other components and means of defining communication linksmay be used.

The computing device 1720 may be primarily designed to include a userinterface. The user interface may include a character, a key-based, oranother user data input via the touch sensitive display 1732. The userinterface may include using a stylus (not shown). Moreover, the userinterface is not limited to an actual touch-sensitive panel arranged fordirectly receiving input, but may alternatively or in addition respondto another input device such as the microphone 1734. For example, spokenwords may be received at the microphone 1734 and recognized.Alternatively, the computing device 1720 may be designed to include auser interface having a physical keyboard (not shown).

The device functional elements 1750 are typically application specificand related to a function of the electronic device, and are coupled withthe system bus 1723 through an interface (not shown). The functionalelements may typically perform a single well-defined task with little orno user configuration or setup, such as a refrigerator keeping foodcold, a cell phone connecting with an appropriate tower and transceivingvoice or data information, a camera capturing and saving an image, orcommunicating with an implantable medical apparatus.

In certain instances, one or more elements of the thin computing device1720 may be deemed not necessary and omitted. In other instances, one ormore other elements may be deemed necessary and added to the thincomputing device.

FIG. 2 and the following discussion are intended to provide a brief,general description of an environment in which embodiments may beimplemented. FIG. 2 illustrates an example embodiment of ageneral-purpose computing system in which embodiments may beimplemented, shown as a computing system environment 1800. Components ofthe computing system environment 1800 may include, but are not limitedto, a general purpose computing device 1810 having a processor 1820, asystem memory 1830, and a system bus 1821 that couples various systemcomponents including the system memory to the processor 1820. The systembus 1821 may be any of several types of bus structures including amemory bus or memory controller, a peripheral bus, and a local bus usingany of a variety of bus architectures. By way of example, and notlimitation, such architectures include Industry Standard Architecture(ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA)bus, Video Electronics Standards Association (VESA) local bus, andPeripheral Component Interconnect (PCI) bus, also known as Mezzaninebus.

The computing system environment 1800 typically includes a variety ofcomputer-readable media products. Computer-readable media may includeany media that can be accessed by the computing device 1810 and includeboth volatile and nonvolatile media, removable and non-removable media.By way of example, and not of limitation, computer-readable media mayinclude computer storage media. By way of further example, and not oflimitation, computer-readable media may include a communication media.

Computer storage media includes volatile and nonvolatile, removable andnon-removable media implemented in any method or technology for storageof information such as computer-readable instructions, data structures,program modules, or other data. Computer storage media includes, but isnot limited to, random-access memory (RAM), read-only memory (ROM),electrically erasable programmable read-only memory (EEPROM), flashmemory, or other memory technology, CD-ROM, digital versatile disks(DVD), or other optical disk storage, magnetic cassettes, magnetic tape,magnetic disk storage, or other magnetic storage devices, or any othermedium which can be used to store the desired information and which canbe accessed by the computing device 1810. In a further embodiment, acomputer storage media may include a group of computer storage mediadevices. In another embodiment, a computer storage media may include aninformation store. In another embodiment, an information store mayinclude a quantum memory, a photonic quantum memory, or atomic quantummemory. Combinations of any of the above may also be included within thescope of computer-readable media. Computer storage media is anon-transitory computer-readable media.

Communication media may typically embody computer-readable instructions,data structures, program modules, or other data in a modulated datasignal such as a carrier wave or other transport mechanism and includeany information delivery media. The term “modulated data signal” means asignal that has one or more of its characteristics set or changed insuch a manner as to encode information in the signal. By way of example,and not limitation, communications media may include wired media, suchas a wired network and a direct-wired connection, and wireless mediasuch as acoustic, RF, optical, and infrared media. Communication mediais a transitory computer-readable media.

The system memory 1830 includes computer storage media in the form ofvolatile and nonvolatile memory such as ROM 1831 and RAM 1832. A RAM mayinclude at least one of a DRAM, an EDO DRAM, a SDRAM, a RDRAM, a VRAM,or a DDR DRAM. A basic input/output system (BIOS) 1833, containing thebasic routines that help to transfer information between elements withinthe computing device 1810, such as during start-up, is typically storedin ROM 1831. RAM 1832 typically contains data and program modules thatare immediately accessible to or presently being operated on by theprocessor 1820. By way of example, and not limitation, FIG. 2illustrates an operating system 1834, application programs 1835, otherprogram modules 1836, and program data 1837. Often, the operating system1834 offers services to applications programs 1835 by way of one or moreapplication programming interfaces (APIs) (not shown). Because theoperating system 1834 incorporates these services, developers ofapplications programs 1835 need not redevelop code to use the services.Examples of APIs provided by operating systems such as Microsoft's“WINDOWS” ® are well known in the art.

The computing device 1810 may also include otherremovable/non-removable, volatile/nonvolatile computer storage mediaproducts. By way of example only, FIG. 2 illustrates a non-removablenon-volatile memory interface (hard disk interface) 1840 that reads fromand writes for example to non-removable, non-volatile magnetic media.FIG. 2 also illustrates a removable non-volatile memory interface 1850that, for example, is coupled to a magnetic disk drive 1851 that readsfrom and writes to a removable, non-volatile magnetic disk 1852, or iscoupled to an optical disk drive 1855 that reads from and writes to aremovable, non-volatile optical disk 1856, such as a CD ROM. Otherremovable/non-removable, volatile/non-volatile computer storage mediathat can be used in the example operating environment include, but arenot limited to, magnetic tape cassettes, memory cards, flash memorycards, DVDs, digital video tape, solid state RAM, and solid state ROM.The hard disk drive 1841 is typically connected to the system bus 1821through a non-removable memory interface, such as the interface 1840,and magnetic disk drive 1851 and optical disk drive 1855 are typicallyconnected to the system bus 1821 by a removable non-volatile memoryinterface, such as interface 1850.

The drives and their associated computer storage media discussed aboveand illustrated in FIG. 2 provide storage of computer-readableinstructions, data structures, program modules, and other data for thecomputing device 1810. In FIG. 2, for example, hard disk drive 1841 isillustrated as storing an operating system 1844, application programs1845, other program modules 1846, and program data 1847. Note that thesecomponents can either be the same as or different from the operatingsystem 1834, application programs 1835, other program modules 1836, andprogram data 1837. The operating system 1844, application programs 1845,other program modules 1846, and program data 1847 are given differentnumbers here to illustrate that, at a minimum, they are differentcopies.

A user may enter commands and information into the computing device 1810through input devices such as a microphone 1863, keyboard 1862, andpointing device 1861, commonly referred to as a mouse, trackball, ortouch pad. Other input devices (not shown) may include at least one of atouch-sensitive screen or display surface, joystick, game pad, satellitedish, and scanner. These and other input devices are often connected tothe processor 1820 through a user input interface 1860 that is coupledto the system bus, but may be connected by other interface and busstructures, such as a parallel port, game port, or a universal serialbus (USB).

A display 1891, such as a monitor or other type of display device orsurface may be connected to the system bus 1821 via an interface, suchas a video interface 1890. A projector display engine 1892 that includesa projecting element may be coupled to the system bus. In addition tothe display, the computing device 1810 may also include other peripheraloutput devices such as speakers 1897 and printer 1896, which may beconnected through an output peripheral interface 1895.

The computing system environment 1800 may operate in a networkedenvironment using logical connections to one or more remote computers,such as a remote computer 1880. The remote computer 1880 may be apersonal computer, a server, a router, a network PC, a peer device, orother common network node, and typically includes many or all of theelements described above relative to the computing device 1810, althoughonly a memory storage device 1881 has been illustrated in FIG. 2. Thenetwork logical connections depicted in FIG. 2 include a local areanetwork (LAN) and a wide area network (WAN), and may also include othernetworks such as a personal area network (PAN) (not shown). Suchnetworking environments are commonplace in offices, enterprise-widecomputer networks, intranets, and the Internet.

When used in a networking environment, the computing system environment1800 is connected to the network 1871 through a network interface, suchas the network interface 1870, the modem 1872, or the wireless interface1893. The network may include a LAN network environment, or a WANnetwork environment, such as the Internet. In a networked environment,program modules depicted relative to the computing device 1810, orportions thereof, may be stored in a remote memory storage device. Byway of example, and not limitation, FIG. 2 illustrates remoteapplication programs 1885 as residing on memory storage device 1881. Itwill be appreciated that the network connections shown are examples andother means of defining a communication link between the computers maybe used.

In certain instances, one or more elements of the computing device 1810may be deemed not necessary and omitted. In other instances, one or moreother elements may be deemed necessary and added to the computingdevice.

FIG. 3 illustrates an example environment 1900 that includes an antenna1910. The antenna includes a sub-Nyquist holographic aperture 1930configured to define at least two selectable, arbitrary complexradiofrequency electromagnetic fields on a surface 1924 with tangentialwavenumbers up to the free-space wavenumber (k₀). The free-spacewavenumber (k₀), sometimes written as k₀ without the parenthesis or ask0, is employed in Fourier optics or Fourier domain theory. Thefree-space wavenumber can be expressed as a function of frequency andvelocity, or just the wavelength:

k ₀=2π/λ

An arbitrary complex radiofrequency electromagnetic field of the atleast two selectable, arbitrary complex radiofrequency electromagneticfields is illustrated by arbitrary complex radiofrequencyelectromagnetic field 1934. In an embodiment, the aperture is physicallyor structurally associated with the surface. For example, a sub-Nyquistholographic aperture may include an aperture with aperture elementsspaced more closely than the Nyquist sampling rate for the operatingfrequency. The surface is configured to receive an incidentradiofrequency electromagnetic wave 1940. The surface is also configuredto transmit or radiate the radiofrequency electromagnetic wave 1942.

In an embodiment, the holographic aperture 1930 includes a sub-Nyquisttransmission hologram-defined aperture. In an embodiment, theholographic aperture includes a sub-Nyquist reflection hologram-definedaperture. In an embodiment, the holographic aperture includes asub-Nyquist scalar holographic aperture. For example, the sub-Nyquistscalar holographic aperture may provide amplitude or phase controlwithout polarization. For example, a sub-Nyquist scalar holographicaperture may be based on scalar Huygens-Fresnel principles. In anembodiment, the holographic aperture includes an amplitude modulationhologram-defined aperture. In an embodiment, the amplitude modulationincludes amplitude modulation by non-negative numbers. In an embodiment,the amplitude modulation includes amplitude modulation by both positiveand negative numbers, and zero. In an embodiment, the holographicaperture includes a sub-Nyquist vector holographic aperture. Forexample, polarization control is expected to provide increased accuracyin the near field. For example, the sub-Nyquist vector holographicaperture may be based on vector diffraction theory, such as theStratton-Chu (a.k.a. Schelkunoff) vector integral transformation.Furthermore, vector diffraction theory ultimately derives from dyadic(tensor) Green's function (propagator) for electromagnetic fields. In anembodiment, the holographic aperture includes a phase modulationholographic aperture. For example, phase modulation may be defined asthe use of at least two phases that are different modulo π (not modulo2π). In an embodiment, the holographic aperture includes an amplitudeand a phase modulation holographic aperture. For example, a classicalradiofrequency example of simultaneous amplitude and phase modulation isQAM—Quadratic Amplitude Modulation, where two amplitudes and two phasesare combined to form a 4-star constellation in the complex plane. Thisexample includes phase shifts of less than π, such as π/2. In anembodiment, the holographic aperture includes a holographic apertureconfigured to dynamically define a series of at least two arbitrarycomplex radiofrequency electromagnetic fields on the surface 1924.

In an embodiment, the antenna 1910 has an operating frequency betweenapproximately 300 GHz and approximately 3 THz. This is generallyreferred to as terahertz or submillimeter radiofrequency electromagneticwaves. In an embodiment, the antenna has an operating frequency lessthan approximately 300 GHz. This is generally referred to as below orless than infrared and Terahertz radiofrequency electromagnetic waves.In an embodiment, the antenna has an operating frequency betweenapproximately 300 MHz and approximately 300 GHz. This is generallyreferred to as millimeter or microwave radiofrequency electromagneticwaves. In an embodiment, the antenna has an operating frequency betweenapproximately 3 Hz and approximately 300 MHz. This is generally referredto as radio electromagnetic waves.

In an embodiment, the antenna 1910 has an operating frequency thatincludes the 60 GHz band. The 60 GHz band is generally consideredbetween 57 and 65 GHz, and may be described as WiGigg communicationsband. In an embodiment, the antenna has an operating frequency thatincludes at least one of the 70 GHz band, the 80 GHz, or the 90 GHzband. The 70 GHz band is generally considered between 71 and 76 GHz. The80 GHz band is generally considered between 81 and 86 GHz. The 90 GHzband is generally considered between 92 and 95 GHz.

In an embodiment, the antenna 1910 is configured to beam radiofrequencyelectromagnetic power. In an embodiment, the antenna is configured totransfer radiofrequency electromagnetic power. In an embodiment, theantenna is configured to receive a radiofrequency electromagnetic wave.In an embodiment, the sub-Nyquist holographic aperture 1930 isconfigured to define a selected arbitrary complex radiofrequencyelectromagnetic field in response to respective electrical controlsignals.

FIG. 4 illustrates an alternative embodiment of the antenna 1910. In thealternative embodiment, the surface 1924 includes a second surface of agenerally planar structure 1920. The planar structure includes a firstsurface 1922 configured to receive incident radiofrequencyelectromagnetic waves 1940. The sub-Nyquist holographic aperture 1930 isconfigured to coherently reconstruct the incident radiofrequencyelectromagnetic waves responsive to a definition on the second surfaceof a selected one 1934 of the at least two selectable, arbitrary complexradiofrequency electromagnetic fields. The second surface is configuredto transmit the coherent reconstruction of the incident radiofrequencyelectromagnetic waves 1942. For example, in an embodiment, thesub-Nyquist holographic aperture functions as a modifying element or asa lens. In an embodiment, the coherent reconstruction includes formationof an antenna gain pattern defined by the selected 1934 selectable,arbitrary complex radiofrequency electromagnetic field. In anembodiment, the antenna gain pattern includes an antenna radiation ortransmission gain pattern. In an embodiment, the antenna gain patternincludes an antenna reception gain pattern.

In an embodiment, the incident radiofrequency electromagnetic wave 1940includes a free space propagating radiofrequency electromagnetic wave.For example, a free space propagating radiofrequency electromagneticwave may include a wave propagating in clear air. In an embodiment, theincident radiofrequency electromagnetic waves include incidentwaveguide-propagated radiofrequency electromagnetic waves. In anembodiment, the wavenumber inside the waveguide exceeds the free spacewavenumber (k₀). In an embodiment, the incident radiofrequencyelectromagnetic waves include radiofrequency electromagnetic wavesleaking from a waveguide. For example, the waveguide may include aplanar waveguide. In an embodiment, the incident radiofrequencyelectromagnetic waves include incident conductor-propagatedradiofrequency electromagnetic waves. In an embodiment, the incidentradiofrequency electromagnetic waves include non-normal incidentradiofrequency electromagnetic waves. For example, a non-normal incidentelectromagnetic wave may be up to 90 degrees off normal, such asparallel to the first surface 1922. For example, clear air may includeclear air within a room, build, warehouse, or stadium. In an embodiment,the incident radiofrequency electromagnetic waves include radiofrequencyelectromagnetic waves propagating oblique to the surface. In anembodiment, the transmitted radiofrequency electromagnetic wave 1942includes a free space propagating radiofrequency electromagnetic wave.

In an embodiment, the generally planar structure 1920 includes agenerally planar curved structure. For example, the generally planarstructure may include a locally flat surface whose principal radii ofcurvature are much larger than the aperture element spacing. For anexample, see aperture element spacing 2018 described in conjunction withFIG. 5 infra. In an embodiment, the generally planar structure includesa generally planar structure having a first surface 1922 and secondsurface 1924 spaced apart from and generally parallel to the firstsurface. In an embodiment, the first surface is spaced apart from thesecond surface by a distance equal to or less than twice a free-spacewavelength corresponding to an operating frequency of the antenna. In anembodiment, the operating frequency includes the highest frequency of anoperating frequency band or bandwidth, or an operating frequency range.In an embodiment, the first surface is spaced apart from the secondsurface by a distance less than four times a free-space wavelengthcorresponding to an operating frequency of the antenna.

In another alternative embodiment of the antenna 1910, the surface is asecond surface 1924 of a generally planar structure. The planarstructure includes a first surface 1922. The second surface isconfigured to receive an incident free-space propagating radiofrequencyelectromagnetic wave 1942. The sub-Nyquist holographic aperture 1930 isconfigured to coherently reconstruct the incident free-spaceradiofrequency electromagnetic wave responsive to a definition on thesecond surface of a selected one 1934 of the at least two selectable,arbitrary complex radiofrequency electromagnetic fields. The firstsurface is configured to transmit the coherent reconstruction 1940 ofthe incident free-space radiofrequency electromagnetic wave 1942.

In an embodiment, the coherent reconstruction 1940 includes formation ofan antenna gain radiation defined by the selected 1934 selectable,arbitrary complex radiofrequency electromagnetic field. In anembodiment, the antenna radiation pattern includes an antennatransmission pattern. In an embodiment, the antenna radiation patternincludes an antenna reception pattern. In an embodiment, the transmittedcoherent reconstruction includes waveguide-propagated transmission ofthe coherent reconstruction of the incident radiofrequencyelectromagnetic wave. In an embodiment, the transmitted coherentreconstruction includes conductor-propagated transmission of thecoherent reconstruction of the incident radiofrequency electromagneticwave. In an embodiment, the at least two selectable, arbitrary complexradiofrequency electromagnetic fields are respectively configured forreception of radiofrequency electromagnetic waves. In an embodiment, theat least two selectable, arbitrary complex radiofrequencyelectromagnetic fields are respectively configured for transmission of aradiofrequency electromagnetic waves. In an embodiment, the at least twoselectable, arbitrary complex radiofrequency electromagnetic fields arerespectively configured for transmission or reception of radiofrequencyelectromagnetic waves.

FIG. 5 illustrates an alternative embodiment 2000 of the antenna 1910.In the alternative embodiment, the sub-Nyquist holographic aperture 1930includes a plurality of individual electromagnetic wave scatteringelements 1300 distributed on or proximate to the surface 1924. Eachscattering element is connected by a bias voltage line 1302 to a biasingcircuit 1304 addressable by row inputs 1306 and column inputs 1308. Eachelectromagnetic wave scattering element has a respective electronicallycontrollable or activatable electromagnetic response to an incidentradiofrequency electromagnetic wave, such as the incident radiofrequencyelectromagnetic wave 1940. The plurality of individual electromagneticwave scattering elements are electronically controllable in combinationto define the at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface 1924. Additional description ofthe plurality of the individual electromagnetic wave scattering elements1300 is provided in U.S. patent application Ser. No. 13/317,388,entitled SURFACE SCATTERING ANTENNAS, naming NATHAN KUNDTZ ET AL. asinventors, filed Oct. 15, 2010, including the technologies described inconjunction with FIG. 13 therein.

In an embodiment, the antenna 1910 includes an electromagnetic waveguidestructure. The plurality of individual electromagnetic wave scatteringelements 1300 are distributed along the waveguide structure with aninter-element spacing substantially less than a free-space wavelength ofa highest operating frequency of the antenna. Each electromagnetic wavescattering element has a respective activatable electromagnetic responseto a guided wave propagating in the waveguide structure, such as theincident radiofrequency electromagnetic wave 1940. The plurality ofelectromagnetic wave scattering elements operable in combination todefine the at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface.

In an embodiment of the antenna 1910, the plurality of individualelectromagnetic wave scattering elements 1300 are periodicallydistributed on the surface 1924. In an embodiment, the plurality ofindividual electromagnetic wave scattering elements includes a pluralityof identical electromagnetic scattering elements. In an embodiment, theplurality of individual electromagnetic wave scattering elementsincludes a plurality of adjustable electromagnetic scattering elements.In an embodiment, the adjustable electromagnetic scattering elements arecontinuously adjustable. In an embodiment, the adjustableelectromagnetic response are discretely adjustable. In an embodiment,the plurality of individual electromagnetic wave scattering elementsincludes a plurality of metamaterial electromagnetic wave scatteringelements. In an embodiment, the plurality of individual electromagneticwave scattering elements include a plurality of individual complementarymetamaterial elements having at least two magnetic dipole responses toincident radiofrequency electromagnetic waves. In an embodiment, theplurality of individual complementary metamaterial electromagnetic wavescattering elements includes a plurality of individual complementaryelectric LC metamaterial elements. In an embodiment, the plurality ofindividual electromagnetic wave scattering elements have atransmissibility controllable by an electronically controllable layer ofliquid crystal respectively disposed on each of the plurality ofindividual electromagnetic wave scattering elements. In an embodiment,the plurality of individual electromagnetic wave scattering elements areembedded within, located on, or located within an evanescent proximityof the surface. In an embodiment, the plurality of individualelectromagnetic wave scattering elements is configured to receive anincident wave from a waveguide. In an embodiment, at least one theplurality of individual electromagnetic wave scattering elements isconfigured to receive an incident wave from a conductor.

In an embodiment, the plurality of individual electromagnetic wavescattering elements 1300 have an inter-element spacing 2018 less thanone-half of a free-space wavelength corresponding to an operatingfrequency of the antenna 1910. In this embodiment, the plurality ofindividual electromagnetic wave scattering elements are spaced moreclosely than Nyquist sampling frequency. In an embodiment, the pluralityof individual electromagnetic wave scattering elements have a periodicinter-element spacing less than one-third of a free-space wavelengthcorresponding to an operating frequency of the antenna. In thisembodiment, the spacing of plurality of individual electromagnetic wavescattering elements may be described as deeply sub-wavelength. In anembodiment, the plurality of individual electromagnetic wave scatteringelements have a periodic inter-element spacing less than one-quarter ofa free-space wavelength corresponding to an operating frequency of theantenna.

In an embodiment, the sub-Nyquist holographic aperture 1930 includes awave-propagating structure, and a plurality of subwavelength patchelements. The plurality of subwavelength patch elements are distributedalong the wave-propagating structure and have inter-element spacingsubstantially less than a free-space wavelength of a highest operatingfrequency of the antenna. Each subwavelength patch element has arespective activatable electromagnetic response to a guided wavepropagating in the wave-propagating structure. The plurality ofsubwavelength patch elements are operable in combination to define theat least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface 1924. Additional description andembodiments of the subwavelength patch elements is provided in U.S.patent application Ser. No. 13/317,388, entitled SURFACE SCATTERINGANTENNAS, naming NATHAN KUNDTZ et al. as inventors, filed Oct. 15, 2010,including the technologies described in conjunction with FIGS. 5-6therein.

In an embodiment, the sub-Nyquist holographic aperture 1930 includes afirst sub-Nyquist holographic aperture and a second sub-Nyquistholographic aperture. The first and second sub-Nyquist holographicapertures are configured in combination to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields onthe surface 1924.

FIG. 6 illustrates an embodiment 2100 of the antenna 1910 wherein afirst sub-Nyquist holographic aperture 1930A and a second sub-Nyquistholographic aperture 1930B are arranged in series to an incidentradiofrequency electromagnetic wave, illustrated by the incidentradiofrequency electromagnetic wave 1940. In an embodiment, the firstsub-Nyquist holographic aperture 1910A is configured to control anamplitude of a radiofrequency electromagnetic wave radiated by thedefined at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface. The second sub-Nyquistholographic aperture 1910B is configured to control a phase of anelectromagnetic wave radiated by the defined at least two selectable,arbitrary complex radiofrequency electromagnetic fields on the surface.In an embodiment, the first sub-Nyquist holographic aperture includes aplurality of individual electromagnetic wave scattering elementsdistributed on the surface, and the second sub-Nyquist holographicaperture includes a plurality of liquid crystal phase control elementsdistributed on the surface. For example, the plurality of individualelectromagnetic wave scattering elements may include the plurality ofindividual electromagnetic wave scattering elements 1300 described inconjunction with FIG. 5. For example, a plurality of liquid crystalphase control elements may provide a variable refractive index biased byarray of quasi-dc electrodes.

Returning to FIGS. 3 and 4, in an embodiment, the holographic aperture1930 and the surface 1924 are configured to receive an incidentradiofrequency electromagnetic wave 1942. In an embodiment, the incidentradiofrequency electromagnetic waves include incident guidedelectromagnetic waves. In an embodiment, the incident radiofrequencyelectromagnetic waves include incident radiofrequency electromagneticwaves propagated or conveyed toward the holographic aperture by awaveguide. In an embodiment, the holographic aperture and the surfaceare configured to transmit a radiofrequency electromagnetic wave 1942into a free space. The transmitted radiofrequency electromagnetic wavecoherently reconstructed by the sub-Nyquist holographic aperture from areceived incident wave and has a radiation pattern defined by a selectedone of the at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields.

In an embodiment, the reactive near-field region can be defined as thevolume of free space consisting of all points located closer than onehalf-wavelength to the nearest point on the field-emitting aperture. Inother words, this is the region where evanescent waves generated byelements spaced less than one-half wavelength apart may be significant.Evanescent waves necessarily become exponentially small beyond thatdistance. In an embodiment, the reactive near-field region can bedefined as the volume of free space consisting of all points locatedcloser than two wavelengths to the nearest point on the field-emittingaperture. In an alternative embodiment, the reactive near-field regioncan be defined as the volume of free space consisting of all pointslocated closer than five wavelengths to the nearest point on thefield-emitting aperture.

In an embodiment, a far-field radiation pattern is defined as theexterior of the sphere of radius R_Fr=2D̂2/lambda (where D is thediameter of the aperture, centered at the centroid of the aperture. Inan embodiment, in strongly scattering environments, such as indoorantennas, the diameter of the aperture D should be taken equal to thediameter of the room. Consequently, generally there are no far-fieldregions inside a room or office; it exists only outside of it. In suchan environment inside the room, the space is divided between reactiveand radiative near-field. In an embodiment, the far-field radiationpattern includes a lobe providing a high gain region optimized totransfer radiofrequency electromagnetic power. The term “diameter” fornon-circular objects is understood as the largest dimension of theobject; for a rectangle, the diameter is equal to its diagonal. In anembodiment, a radiative near-field is defined as all volume that isneither far-field nor reactive near-field.

In an embodiment, the sub-Nyquist holographic aperture 1930 isconfigured to define at least two selectable, arbitrary complexradiofrequency electromagnetic fields on the surface 1924. Eachelectromagnetic field respectively describes a far-field electromagneticradiation pattern. In an embodiment, a far-field radiation patternincludes a Fraunhofer region radiation pattern. In an embodiment, eacharbitrary complex radiofrequency electromagnetic field respectivelyproduces a radiofrequency electromagnetic radiation pattern. In anembodiment, an antenna radiation pattern includes a representation ofthe angular distribution of the power density produced in the far-fieldregion. In an embodiment, an antenna radiation pattern includeselectromagnetic radiation or electromagnetic peaks in directions otherthan normal to the surface. In an embodiment, an antenna radiationpattern includes steerable beam. In an embodiment, an antenna radiationpattern includes near-field focusing. In an embodiment, each arbitrarycomplex radiofrequency electromagnetic field respectively produces aradiofrequency electromagnetic antenna transmission pattern. In anembodiment, each arbitrary complex radiofrequency electromagnetic fieldrespectively produces a radiofrequency electromagnetic antenna receptionpattern. In an embodiment, the each arbitrary complex radiofrequencyelectromagnetic field respectively describes a high gain regionconfigured to transfer electromagnetic power to a target device. In anembodiment, each arbitrary complex radiofrequency electromagnetic fieldrespectively describes a far-field radiation pattern having a lobeproviding a high radiofrequency electromagnetic radiation patternconfigured to transfer electromagnetic power to a target device in thefar-field region. In an embodiment, the radiofrequency electromagneticradiation pattern is configured to transfer electromagnetic power havinga maximum density to a target device in the far-field region. In anembodiment, the radiofrequency electromagnetic radiation pattern isconfigured to transfer electromagnetic power to the target device in thefar-field region with a maximum efficiency. In an embodiment, theradiofrequency electromagnetic radiation pattern is optimized totransfer electromagnetic power having a maximum density to the targetdevice in the far-field region while subject to a constraint minimizingor limiting a transfer of electromagnetic radiation power transferred toanother portion of the far-field region. In an embodiment, theradiofrequency electromagnetic radiation pattern is optimized totransfer electromagnetic power to the target device in the far-fieldregion, the optimization responsive to a set of configurable rules. Inan embodiment, the set of configurable rules is responsive to criteriato minimize or limit a transfer of electromagnetic radiation powertransferred to another far-field region. In an embodiment, theradiofrequency electromagnetic radiation pattern is optimized totransfer electromagnetic power to the target device in the far-fieldregion. The optimization is responsive to a comparison ofelectromagnetic radiation power transferred to the target device againstelectromagnetic radiation power transferred to another region whereelectromagnetic radiation power is subjected to limit or constraint.

In an embodiment, the holographic aperture 1930 includes a sub-Nyquistholographic aperture configured to define at least two selectable,arbitrary complex radiofrequency electromagnetic fields on the surface1924. Each electromagnetic field of the at least two radiofrequencyelectromagnetic fields respectively describes a radiative near-fieldelectromagnetic radiation pattern. In an embodiment, each arbitrarycomplex radiofrequency electromagnetic field respectively describes aradiofrequency electromagnetic radiation pattern configured to transferelectromagnetic power to a target device. In an embodiment, eacharbitrary complex radiofrequency electromagnetic field respectivelydescribes a quasi-Gaussian electromagnetic beam having a radiativenear-field distribution configured to transfer electromagnetic power toa target device in the radiative near-field. In an embodiment, eacharbitrary complex radiofrequency electromagnetic field respectivelydescribes a radiofrequency electromagnetic radiation pattern configuredto transfer electromagnetic power to a target device by a localizationof the electromagnetic field to the target device. For example, eacharbitrary complex radiofrequency electromagnetic field may respectivelydescribe a radiofrequency electromagnetic radiation pattern configuredto transfer electromagnetic power to a target device by transverselocalization of the electromagnetic field to an antenna aperture of thetarget device.

In an embodiment, the holographic aperture 1930 includes a sub-Nyquistholographic aperture configured to define at least two selectable,arbitrary complex radiofrequency electromagnetic fields on the surface1924. Each electromagnetic field of the at least two radiofrequencyelectromagnetic fields respectively describes a reactive near-fieldelectromagnetic radiation pattern. The reactive near-fieldelectromagnetic radiation pattern may be a two or a three dimensionalradiation pattern. In an embodiment, each arbitrary complexradiofrequency electromagnetic field respectively describes aradiofrequency electromagnetic radiation pattern transversely localizedto transfer electromagnetic power to a target device. For example, adimension of the holographic aperture may be tailored and positioned tocoincide with a dimensions or a location of a target device. In anembodiment, each arbitrary complex radiofrequency electromagnetic fielddescribes a reactive near-field electromagnetic radiation patterngenerally defined at the surface and configured to electromagneticallycouple with a target device located within one-half of the wavelength ofthe surface. In an embodiment, each arbitrary complex radiofrequencyelectromagnetic field respectively describing a reactive near-fieldsub-wavelength electromagnetic field pattern having a predominantlymagneto-inductive nature. For example, magneto-inductive power transferincludes a transfer of power generated by a metamaterial apertureoperating near the frequency of magnetic dipole resonances for themajority of the unit cells. In an embodiment, each arbitrary complexradiofrequency electromagnetic field includes tangential wavenumbersbeyond the free-space wavenumber (k₀). In an embodiment, each arbitrarycomplex radiofrequency electromagnetic field respectively describing areactive near-field sub-wavelength electromagnetic field patternoptimized to transfer electromagnetic power to a target device presentin the reactive near-field. In an embodiment, the holographic apertureincludes a sub-Nyquist vector holographic aperture configured to defineat least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface.

In an embodiment, the holographic aperture 1930 includes at least twoindependently operable sub-Nyquist holographic apertures. Eachsub-Nyquist holographic aperture is respectively configured to definethe at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on a portion of the surface 1924. In anembodiment, the antenna 1910 includes a radiofrequency beam-formingsub-Nyquist holographic aperture configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields onthe surface. In an embodiment, the at least two independently operablesub-Nyquist holographic apertures are interlaced. In an embodiment, theat least two independently operable sub-Nyquist holographic aperturesare dynamically reconfigurable areas of holographic aperture.

FIG. 7 illustrates an example operational flow 2200. After a startoperation, the operational flow includes an antenna gain operation 2210.The antenna gain operation includes defining a selected arbitrarycomplex radiofrequency electromagnetic field on a surface, the selectedarbitrary complex radiofrequency electromagnetic field having tangentialwavenumbers up to the free-space wavenumber (k₀). The arbitrary complexradiofrequency electromagnetic field is selected from at least twoselectable, arbitrary complex radiofrequency electromagnetic fields. Inan embodiment, the antenna gain operation may be implemented using thesub-Nyquist holographic aperture 1930 described in conjunction withFIGS. 3-4. A reception operation 2220 includes receiving incidentradiofrequency electromagnetic waves. In an embodiment, the receptionoperation may be implemented using the first surface 1922 of the antenna1910 to receive the incident radiofrequency electromagnetic wave 1940 asdescribed in conjunction with FIGS. 3-4. A transmission operation 2230includes radiating radiofrequency electromagnetic waves coherentlyreconstructed from the incident radiofrequency electromagnetic waves bythe selected arbitrary complex radiofrequency electromagnetic fielddefined on the surface. In an embodiment, the transmission operation maybe implemented using second surface 1924 of the antenna to transmit theradiofrequency electromagnetic wave 1942 as described in conjunctionwith FIGS. 3-4. The operational flow includes an end operation.

In an embodiment, the antenna gain operation 2210 includes defining aselected arbitrary complex radiofrequency electromagnetic field on thesurface using a sub-Nyquist holographic aperture. The sub-Nyquistholographic aperture is configured to define at least two selectable,arbitrary complex radiofrequency electromagnetic fields on the surface.In an embodiment, the sub-Nyquist holographic aperture includes ametamaterial sub-Nyquist holographic aperture.

In an embodiment, the reception operation 2220 includes receivingincident radiofrequency electromagnetic waves on the surface. In anembodiment, the transmission operation 2230 includes radiating thecoherently reconstructed electromagnetic waves from the surface. In anembodiment, the incident radiofrequency electromagnetic waves includeencoded incident radiofrequency electromagnetic waves. For example, theincident radiofrequency electromagnetic wave may be encoded bymodulation, time division, frequency division, multiplexing, timedivision multiple access, or code division multiple access.

In an embodiment, the operational flow 2200 further includes selectingthe arbitrary complex radiofrequency electromagnetic field from at leasttwo selectable, arbitrary complex radiofrequency electromagnetic fieldswith tangential wavenumbers up to the free-space wavenumber (k₀). In anembodiment, the operational flow includes selecting the arbitrarycomplex radiofrequency electromagnetic field in response to a locationof a particular field of view. In an embodiment, the operational flowincludes selecting the arbitrary complex radiofrequency electromagneticfield in response to a location of an undesired field of view. In anembodiment, each arbitrary complex radiofrequency electromagnetic fieldrespectively describes a desired far-field radiofrequencyelectromagnetic radiation pattern. In an embodiment, each arbitrarycomplex radiofrequency electromagnetic field respectively describes aradiative near-field electromagnetic radiation pattern. In anembodiment, each arbitrary complex radiofrequency electromagnetic fieldrespectively describes a reactive near-field radiofrequencyelectromagnetic radiation pattern.

In an embodiment, the incident radiofrequency electromagnetic wavesinclude encoded incident radiofrequency electromagnetic waves. In anembodiment, the incident radiofrequency electromagnetic waves includeincident free space propagating radiofrequency electromagnetic waves. Inan embodiment, the incident radiofrequency electromagnetic waves includeincident waveguide-propagated radiofrequency electromagnetic waves. Inan embodiment, the incident radiofrequency electromagnetic waves includeincident conductor-propagated radiofrequency electromagnetic waves. Inan embodiment, the incident radiofrequency electromagnetic waves includenon-normal incident radiofrequency electromagnetic waves. In anembodiment, the radiated electromagnetic waves include free spacepropagating radiofrequency electromagnetic waves. In an embodiment, theradiated electromagnetic waves include waveguide-propagatedradiofrequency electromagnetic waves. In an embodiment, the radiatedradiofrequency electromagnetic waves include conductor-propagatedradiofrequency electromagnetic waves.

In an embodiment, the operational flow 2200 includes defining anotherselected arbitrary complex radiofrequency electromagnetic field on thesurface. The other arbitrary complex radiofrequency electromagneticfield is selected from the at least two selectable, arbitrary complexradiofrequency electromagnetic fields. This embodiment also includesradiating additional radiofrequency electromagnetic waves coherentlyreconstructed from the incident radiofrequency electromagnetic waves bythe other selected arbitrary complex radiofrequency electromagneticfield defined on the surface.

FIG. 8 illustrates an example apparatus 2300. The apparatus includesmeans 2310 for selecting an arbitrary complex radiofrequencyelectromagnetic field from the at least two selectable, arbitrarycomplex radiofrequency electromagnetic fields having tangentialwavenumbers up to the free-space wavenumber (k₀). The apparatus includesmeans 2320 for defining the selected arbitrary complex radiofrequencyelectromagnetic field on a surface of an antenna. The apparatus includesmeans 2330 for receiving incident radiofrequency electromagnetic waves.The apparatus includes means 2340 for radiating radiofrequencyelectromagnetic waves coherently reconstructed from the incidentradiofrequency electromagnetic waves by the selected arbitrary complexradiofrequency electromagnetic field defined on the surface.

FIG. 9 illustrates an example operational flow 2400. After a startoperation, the example operational flow includes a reception operation2410. The reception operation includes receiving incident radiofrequencyelectromagnetic waves at a first surface of a generally planar structurethat includes the first surface and a second surface. In an embodiment,the reception operation may be implemented using the first surface 1922of the antenna 1910 to receive the incident radiofrequencyelectromagnetic wave 1940 as described in conjunction with FIG. 4. Anantenna gain operation 2420 includes defining a selected arbitrarycomplex radiofrequency electromagnetic field on the second surface. Theselected arbitrary complex radiofrequency electromagnetic field havingtangential wavenumbers up to the free-space wavenumber (k₀). In anembodiment, the antenna gain operation may be implemented using thesub-Nyquist holographic aperture 1930 and the second surface 1934described in conjunction with FIG. 4. A transmission operation 2430includes radiating from the second surface radiofrequencyelectromagnetic waves coherently reconstructed from the incidentradiofrequency electromagnetic waves by the selected arbitrary complexradiofrequency electromagnetic field. In an embodiment, the transmissionoperation may be implemented using second surface 1924 of the antenna totransmit the radiofrequency electromagnetic wave 1942. The operationalflow includes an end operation.

In an embodiment of the antenna gain operation 2420, the definingincludes defining the selected arbitrary complex radiofrequencyelectromagnetic field on the second surface using a sub-Nyquistholographic aperture. In an embodiment, the sub-Nyquist holographicaperture includes a metamaterial sub-Nyquist holographic aperture. In analternative embodiment, the operational flow further includes selectingthe arbitrary complex radiofrequency electromagnetic field from the atleast two selectable, arbitrary complex radiofrequency electromagneticfields having tangential wavenumbers up to the free-space wavenumber(k₀).

FIG. 10 illustrates an example apparatus 2500. The apparatus includesmeans 2510 for receiving incident radiofrequency electromagnetic wavesat a first surface of a generally planar structure having the firstsurface and a second surface. The apparatus includes means 2520 fordefining a selected arbitrary complex radiofrequency electromagneticfield on the second surface. The selected arbitrary complexradiofrequency electromagnetic field having tangential wavenumbers up tothe free-space wavenumber (k₀). The apparatus includes means 2530 forradiating radiofrequency electromagnetic waves coherently reconstructedfrom the incident radiofrequency electromagnetic waves by the selectedarbitrary complex radiofrequency electromagnetic field defined on thesecond surface. In an embodiment, the apparatus includes means forselecting the arbitrary complex radiofrequency electromagnetic fieldfrom the at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields having tangential wavenumbers up to thefree-space wavenumber (k₀).

FIG. 11 illustrates an example environment 2600 that includes an antenna2610. The antenna includes a sub-Nyquist complex-holographic aperture2630 configured to define at least two selectable, arbitrary complexradiofrequency electromagnetic fields with tangential wavenumbers up to2π over the aperture element spacing (k_apt=2π/a) on a surface 2624. Forexample, see an illustration of an aperture element spacing 2718described in conjunction with FIG. 12 infra. The sub-Nyquistcomplex-holographic aperture 2630 address both cases where the antennaaperture D>>lambda and where D<<lambda. When D>>lambda, reactive andradiative near-field are controlled. When D<<lambda, field profiles inthe reactive near-field are controlled, which provides evanescent wavecontrol and evanescent waves optimized for reactive near-field.

In an embodiment, the sub-Nyquist complex-holographic aperture 2600includes a sub-Nyquist transmission complex-holographic aperture. In anembodiment, the sub-Nyquist complex-holographic aperture includes asub-Nyquist reflective complex-holographic aperture. In an embodiment,the sub-Nyquist complex-holographic aperture includes a sub-Nyquistamplitude and phase modulation holographic aperture.

FIG. 12 illustrates an alternative embodiment of the environment 2700that includes an antenna 2710. The sub-Nyquist complex-holographicaperture 2730 includes the plurality of individual electromagnetic wavescattering elements 1300 distributed on the surface 2624. An example ofthe plurality of individual electromagnetic wave scattering elements isdescribed in conjunction with FIG. 5, including where each scatteringelement is connected by a bias voltage line 1302 to a biasing circuit1304 addressable by row inputs 1306 and column inputs 1308. Eachelectromagnetic wave scattering element has a respective electronicallycontrollable electromagnetic response to an incident radiofrequencyelectromagnetic wave 2640. The plurality of individual electromagneticwave scattering elements are electronically controllable in combinationto define the at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface.

The plurality of individual electromagnetic wave scattering elements1300 are illustrated as each having an aperture spacing “a,” illustratedas inter-element spacing 2718. In an embodiment, the aperture spacing isa center-to-center spacing distance between at least two individualelectromagnetic scattering elements of the plurality of individualelectromagnetic wave scattering elements. In this alternativeembodiment, the wavenumber is the inverse of the aperture spacing(k_apt=2π/a).

In an embodiment, the antenna 2710 includes at least two electromagneticwave conducting structures respectively coupled to at least twoindividual electromagnetic wave scattering elements of the plurality ofindividual electromagnetic wave scattering elements 1300. In anembodiment, the incident radiofrequency electromagnetic waves 2640include incident wave guide-propagated electromagnetic waves. In anembodiment, the incident radiofrequency electromagnetic waves includeincident conductor-propagated electromagnetic waves.

In an embodiment, the surface includes a second surface 2624 of agenerally planar structure 2620. The planar structure including a firstsurface 2622 configured to receive incident radiofrequencyelectromagnetic waves 2640. The sub-Nyquist holographic aperture 2630 isconfigured to coherently reconstruct the incident radiofrequencyelectromagnetic waves responsive to a definition on the second surfaceof a selected one 2364 (see FIG. 11) of the at least two selectable,arbitrary complex radiofrequency electromagnetic fields. The secondsurface is configured to transmit the coherent reconstruction 2642 ofthe incident radiofrequency electromagnetic waves. In an embodiment, theincident radiofrequency electromagnetic waves 2640 includeradiofrequency electromagnetic waves leaking from a planar waveguide. Inan embodiment, the radiated electromagnetic waves includes free spacepropagating electromagnetic waves. In an embodiment, the transmittedcoherent reconstruction 2642 of the incident radiofrequencyelectromagnetic waves includes free space propagating radiofrequencyelectromagnetic waves. In an embodiment, the transmitted coherentreconstruction of the incident radiofrequency electromagnetic wavesincludes waveguide-propagating radiofrequency electromagnetic waves. Inan embodiment, the transmitted coherent reconstruction of the incidentradiofrequency electromagnetic waves includes conductor-propagatingradiofrequency electromagnetic waves.

Returning to FIG. 11, in an embodiment, the generally planar surface2624 includes a generally planar curved surface. In an embodiment, thegenerally planar surface includes a generally planar structure having afirst surface and second surface spaced apart from and generallyparallel to the first surface.

In an embodiment, the sub-Nyquist complex-holographic aperture 2630includes a plurality of individual electromagnetic wave scatteringelements distributed on the surface 2624. Each electromagnetic wavescattering element has a respective electronically controllableelectromagnetic response to an incident radiofrequency electromagneticwave 2640. The plurality of individual electromagnetic wave scatteringelements are electronically controllable in combination to define the atleast two selectable, arbitrary complex radiofrequency electromagneticfields on the surface. In an embodiment, the plurality of individualelectromagnetic wave scattering elements are embedded within, locatedon, or located within an evanescent proximity of the surface 2624.

In an embodiment, the sub-Nyquist complex-holographic aperture 2630includes a first sub-Nyquist complex-holographic aperture and a secondsub-Nyquist complex-holographic aperture. The first and secondsub-Nyquist complex holographic apertures are configured in combinationto define at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface 2624 with tangential wavenumbersup to 2π over the aperture element spacing (k_apt=2π/a). In anembodiment, the first sub-Nyquist complex-holographic aperture and thesecond sub-Nyquist complex-holographic aperture are configured to beencountered in series by incident radiofrequency electromagnetic waves2640. For example, see FIG. 6. In an embodiment, the first sub-Nyquistcomplex-holographic is further configured to control an amplitude ofelectromagnetic waves 2642 radiated in response to an arbitrary complexradiofrequency electromagnetic field defined on the surface. The secondsub-Nyquist complex-holographic aperture is further configured tocontrol a phase of electromagnetic radiofrequency waves radiated inresponse to an arbitrary complex radiofrequency electromagnetic fieldsdefined on the surface. In an embodiment, the first sub-Nyquistcomplex-holographic is includes a plurality of individualelectromagnetic wave scattering elements distributed on the surface. Thesecond sub-Nyquist complex-holographic aperture includes a plurality ofliquid crystal phase control elements distributed on the surface.

In an embodiment, each electromagnetic field respectively describes anear-field radiative electromagnetic radiation pattern. In anembodiment, each near-field radiative radiofrequency electromagneticradiation pattern is respectively configured to transmit radiofrequencyelectromagnetic power to a target device. In an embodiment, eachnear-field radiative radiofrequency electromagnetic radiation patternrespectively describes a quasi-Gaussian electromagnetic beam having aradiative near-field distribution configured to transmit radiofrequencyelectromagnetic power to a target device. In an embodiment, eachradiofrequency electromagnetic field describes a near-field reactiveradiofrequency electromagnetic radiation pattern. In an embodiment, eachnear-field reactive radiofrequency electromagnetic radiation patternrespectively describes a reactive near-field sub-wavelengthradiofrequency electromagnetic field pattern having a predominantlymagneto-inductive nature. In an embodiment, each near-field reactiveradiofrequency electromagnetic radiation pattern is respectivelyconfigured to transfer radiofrequency electromagnetic power to a targetdevice.

In an embodiment, the sub-Nyquist complex-holographic aperture 2630 andthe surface 2624 are configured to transmit electromagnetic waves 2642into free space. The transmitted electromagnetic waves are coherentlyreconstructed by the sub-Nyquist complex-holographic aperture from thereceived incident waves 2640 and have a radiation pattern defined by theselected one 2634 of the at least two selectable, arbitrary complexradiofrequency electromagnetic fields.

FIG. 13 illustrates an example operational flow 2800. After a startoperation, the operational flow includes a reception operation 2810. Thereception operation includes receiving incident radiofrequencyelectromagnetic waves. In an embodiment, the reception operation may beimplemented using the surface 2624 described in conjunction with FIG.11, or the surface 1922 described in conjunction with FIG. 4. An antennagain operation 2820 includes defining a selected arbitrary complexradiofrequency electromagnetic field on a surface using a sub-Nyquistcomplex-holographic aperture. The sub-Nyquist complex-holographicaperture is configured to define at least two selectable, arbitrarycomplex radiofrequency electromagnetic fields on the surface withtangential wavenumbers up to 2π over the aperture element spacing(k_apt=2π/a). The arbitrary complex radiofrequency electromagnetic fieldis selected from at least two selectable, arbitrary complexradiofrequency electromagnetic fields. In an embodiment, the antennagain operation may be implemented using the sub-Nyquist holographicaperture 2630 described in conjunction with FIG. 11. A transmissionoperation 2830 includes transmitting a radiofrequency electromagneticwave coherently reconstructed from the incident radiofrequencyelectromagnetic wave by the selected arbitrary complex radiofrequencyelectromagnetic field defined on the surface. In an embodiment, thetransmission operation may be implemented using the second surface 2624of the antenna 2610 to radiate the radiofrequency electromagnetic wave2642 described in conjunction with FIG. 11. The operational flowincludes an end operation.

In an embodiment, each radiofrequency electromagnetic field respectivelydescribes a radiative near-field electromagnetic radiation pattern. Inan embodiment, each radiofrequency electromagnetic field respectivelydescribes a reactive near-field electromagnetic radiation pattern. In anembodiment, the sub-Nyquist complex-holographic aperture includes ametamaterial sub-Nyquist complex-holographic aperture.

In an embodiment, the operational flow 2800 further includes selecting2840 the arbitrary complex radiofrequency electromagnetic field from theat least two selectable, arbitrary complex radiofrequencyelectromagnetic fields. In an embodiment, the operational flow furtherincludes defining another selected arbitrary complex radiofrequencyelectromagnetic field on the surface using the sub-Nyquistcomplex-holographic aperture. The other arbitrary complex radiofrequencyelectromagnetic field is selected from the at least two selectable,arbitrary complex radiofrequency electromagnetic fields. In thisembodiment, the operational flow also includes transmitting additionalradiofrequency electromagnetic waves coherently reconstructed from theincident radiofrequency electromagnetic waves by the other selectedarbitrary complex radiofrequency electromagnetic field defined on thesurface.

FIG. 14 illustrates an example apparatus 2900. The apparatus includesmeans 2910 for receiving incident radiofrequency electromagnetic waves.The apparatus includes means 2920 for defining a selected arbitrarycomplex radiofrequency electromagnetic field on a surface withtangential wavenumbers up to 2π over the aperture element spacing(k_apt=2π/a). The arbitrary complex radiofrequency electromagnetic fieldis selected from at least two selectable, arbitrary complexradiofrequency electromagnetic fields. The apparatus includes means 2930for transmitting radiofrequency electromagnetic waves coherentlyreconstructed from the incident radiofrequency electromagnetic waves bythe selected arbitrary complex radiofrequency electromagnetic fielddefined on the surface. In an embodiment, the apparatus includes means2940 for selecting the arbitrary complex radiofrequency electromagneticfield from the at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields.

FIG. 15 includes an example operational flow 3000. After a startoperation, the example operational flow includes a reception operation3010. The reception operation includes receiving radiofrequencyelectromagnetic waves at a first surface of a generally planar structurehaving the first surface and a second surface. In an embodiment, thereception operation may be implemented using the first surface 2622 ofthe antenna 2610 to receive the incident radiofrequency electromagneticwave 2640 as described in conjunction with FIG. 11. An antenna gainoperation 3020 includes defining a selected arbitrary complexradiofrequency electromagnetic field on the second surface using asub-Nyquist complex-holographic aperture. The sub-Nyquistcomplex-holographic aperture is configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields onthe second surface with tangential wavenumbers up to 2π over theaperture element spacing (k_apt=2π/a). The arbitrary complexradiofrequency electromagnetic field is selected from at least twoselectable, arbitrary complex radiofrequency electromagnetic fields. Inan embodiment, the antenna gain operation may be implemented using thesub-Nyquist holographic aperture 2630 and the second surface 2634described in conjunction with FIG. 11. A transmission operation 3030includes transmitting from the second surface radiofrequencyelectromagnetic waves coherently reconstructed from the receivedradiofrequency electromagnetic waves by the selected arbitrary complexradiofrequency electromagnetic field defined by the sub-Nyquist complexholographic aperture on the second surface. In an embodiment, thetransmission operation may be implemented using second surface 2624 ofthe antenna 2610 to transmit the radiofrequency electromagnetic wave2642. The operational flow includes an end operation.

In an embodiment, the operational flow 3000 further includes selecting3040 the arbitrary complex radiofrequency electromagnetic field from theat least two selectable, arbitrary complex radiofrequencyelectromagnetic fields.

FIGS. 16 and 17 illustrate an embodiment. FIG. 16 illustrates certainaspects of an environment 3100, and a system 3105. The system includesan antenna 3110 and associated apparatus 3150. The environment includesat least one target device configured to receive wirelessly transferredradiofrequency electromagnetic waves or power. The at least one targetdevice is illustrated by a mobile or handheld smart phone 3190A, and alaptop or tablet or similar device 3190B, and will generically referredto herein as the target device 3190. The environment includes a humanbeing 3198. The environment includes a radiateable space 3102. Forexample, a radiateable space includes any space into which the antennais capable of radiating radiofrequency electromagnetic waves. In anembodiment, the radiateable space may include any environment in whichthe target device and the human being have a presence. The radiateablespace may include a bounded environment. For example and withoutlimitation, in certain embodiments, the radiateable space may include aportion of a residential premises or the entire residential premises.The premises may be under control of one or more persons, such as anindividual or a family. In other embodiments, the radiateable space mayinclude a portion of a business premises, an entire business premises,or a public space. For example, a public space may include an airport,or sports stadium. The radiateable space includes at least two possibleradiofrequency electromagnetic wave radiation or transmission pathways3180. The at least two pathways are illustrated by pathways 3180A-3180E.Pathway 3180A includes a reflection off a surface 3196.

The antenna 3110 includes a sub-Nyquist holographic aperture 3130configured to define at least two selectable, arbitrary complexradiofrequency electromagnetic fields on a surface of the antenna,illustrated as a second surface 3124, over an operating frequency. In anembodiment, the antenna includes a generally planar structure 3120having a first surface 3122, the second surface 3124, and thesub-Nyquist holographic aperture.

FIG. 17 illustrates an embodiment of the associated apparatus 3150. Theassociated apparatus includes a path analysis engine 3152 configured torespectively test at least two power transmission pathways 3180,illustrated as the pathways 3180A-3180E, from the antenna 3110 to atarget device 3190 located in the environment 3100 and within theradiateable space 3102 by the antenna 3110. The environment includes thehuman being 3198. In an embodiment, an engine, such as the path analysisengine, may include a circuit or apparatus that performs a fundamentalfunction, and often a repetitive function, especially as part of alarger system or apparatus. In an embodiment, an engine may coordinateor operate other components or elements of a system or apparatus, suchas the system 3105. In an embodiment, an engine may include one or morecomponents interacting with other elements or devices in operation of asystem or apparatus.

The associated apparatus 3150 includes an optimization circuit 3154configured to select responsive to the tested at least two powertransmission pathways a wireless power transmission regime. The wirelesspower transmission regime includes an electromagnetic radiation patternshaped to wirelessly transfer radiofrequency electromagnetic power fromthe antenna to the target device without exceeding a radiofrequencyelectromagnetic wave radiation exposure limit for human beings. Forexample, compliance with the radiofrequency electromagnetic waveradiation exposure limit may be by avoiding or mostly avoiding the humanbeing so that the limit is not exceeded at the human being 3198. Forexample, compliance with the radiofrequency electromagnetic waveradiation exposure limit may be met by not exceeding the limit anywherein the radiateable space 3102. The system apparatus include a gaindefinition circuit 3154 configured to select a complex radiofrequencyelectromagnetic field implementing the selected wireless powertransmission regime from the at least two selectable, arbitrary complexradiofrequency electromagnetic fields. The system apparatus include anantenna controller 3156 configured to define the selected arbitrarycomplex electromagnetic field 3134 in the sub-Nyquist holographicaperture 3130. In an embodiment, the sub-Nyquist holographic apertureand the surface are cooperatively structured so that radiofrequencyelectromagnetic waves incident upon the surface are coherentlyreconstructed by the selected arbitrary, complex radiofrequencyelectromagnetic field and transmitted to the target device by theaperture. In an embodiment, the sub-Nyquist holographic aperture and thesurface are structured to cooperatively transmit electromagnetic wavesinto free space. The transmitted electromagnetic waves are coherentlyreconstructed by the sub-Nyquist holographic aperture from receivedincident waves and have a radiation pattern defined by the selectedarbitrary complex radiofrequency electromagnetic field.

In an embodiment, the associated apparatus 3150 further includes aradiofrequency electromagnetic wave generating apparatus 3172 configuredto generate and deliver radiofrequency electromagnetic waves to thesurface 3124 of the antenna 3110. The frequency of the radiofrequencyelectromagnetic waves are within at least a portion of the operatingfrequency of the antenna.

In an embodiment, the sub-Nyquist holographic aperture 3130 isconfigured to define at least two selectable, arbitrary complexradiofrequency electromagnetic fields on a surface 3124 with tangentialwavenumbers up to the free-space wavenumber (k₀). In an embodiment, thesub-Nyquist holographic aperture is configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields onthe surface 3124 with tangential wavenumbers up to 2π over the aperturespacing (k_apt=2π/a). In an embodiment, the sub-Nyquist holographicaperture includes an electronically reconfigurable sub-Nyquistholographic aperture configured to dynamically define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields on asurface over an operating frequency. In an embodiment, the sub-Nyquistholographic aperture is configured to define an amplitude of anelectromagnetic wave transmitted by at least two selectable, arbitrarycomplex radiofrequency electromagnetic fields. In an embodiment, thesub-Nyquist holographic aperture is configured to define a phase of anelectromagnetic wave transmitted by at least two selectable, arbitrarycomplex radiofrequency electromagnetic fields.

In an embodiment, the surface 3134 includes a second surface of agenerally planar structure 3120 having a first surface 3122 configuredto receive incident radiofrequency electromagnetic waves. Thesub-Nyquist holographic aperture 3130 is configured to coherentlyreconstruct the incident radiofrequency electromagnetic waves responsiveto a definition on the second surface of a selected 3134 arbitrarycomplex radiofrequency electromagnetic field. The second surface isconfigured to transmit the coherent reconstruction of the incidentradiofrequency electromagnetic waves.

In an embodiment, the antenna 3110 includes at least two independentlyoperable sub-Nyquist holographic apertures 3130. Each sub-Nyquistholographic aperture is respectively configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields on arespective portion of the surface 3124 over an operating frequency. Inan embodiment, a second sub-Nyquist holographic aperture of the at theat least two independently operable sub-Nyquist holographic apertures isconfigured to receive a signal from a target device on a frequency beingtransmitted on by a first sub-Nyquist holographic aperture of the atleast two independently operable sub-Nyquist holographic apertures.

In an embodiment, the antenna 3110 includes at least two orthogonalsub-Nyquist holographic apertures 3130. Each sub-Nyquist holographicaperture respectively configured to define at least two selectable,arbitrary complex radiofrequency electromagnetic fields on a respectiveportion of the surface 3124 over an operating frequency. In anembodiment, each of the at least two orthogonal sub-Nyquist holographicapertures have a respective distinct input. In an embodiment, the atleast two orthogonal sub-Nyquist holographic apertures have a respectivedistinct output.

In an embodiment, the sub-Nyquist holographic aperture 3130 and theassociated apparatus 3150 are configured to (i) define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields on asurface 3124 over an operating frequency and (ii) operate in a singlechannel, full-duplex mode. In an embodiment, the sub-Nyquist holographicaperture 3130 includes a sub-Nyquist holographic aperture configured todefine at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface 3124. Each arbitrary complexradiofrequency electromagnetic field respectively describing a far-fieldelectromagnetic radiation pattern over an operating frequency. In anembodiment, the sub-Nyquist holographic aperture includes a sub-Nyquistholographic aperture configured to define at least two selectable,arbitrary complex radiofrequency electromagnetic fields on the surface.Each arbitrary complex radiofrequency electromagnetic field respectivelydescribing a near-field electromagnetic radiation pattern over anoperating frequency. In an embodiment, the sub-Nyquist holographicaperture includes a sub-Nyquist holographic aperture configured todefine at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface. Each arbitrary complexradiofrequency electromagnetic field respectively describing a reactivenear-field electromagnetic radiation pattern over an operatingfrequency.

In an embodiment, the path analysis engine 3152 is configured to test arespective characteristic of the at least two power transmissionpathways 3180. In an embodiment, the characteristic includes arespective propagation characteristic. In an embodiment, the propagationcharacteristic includes an estimated or measured respectiveradiofrequency channel characteristic. In an embodiment, the propagationcharacteristic includes an estimated or measured respective propagationcharacteristic. In an embodiment, the propagation characteristicincludes a pathway loss. For example, a pathway loss may include apathway loss responsive to distance, absorption, or obstructions. In anembodiment, the propagation characteristic includes a reflectioncharacteristic. For example a reflection characteristic may include areflection characteristic of the surface 3196. For example a reflectioncharacteristic may include a reflection characteristic of an obstructionor a surface irregularity. In an embodiment, the propagationcharacteristic includes a refraction or diffraction characteristic. Inan embodiment, the propagation characteristic includes a phase changecharacteristic. In an embodiment, the propagation characteristicincludes a time delay characteristic. In an embodiment, the propagationcharacteristic includes a time varying characteristic. In an embodiment,the propagation characteristic includes overall transmission efficiencycharacteristic. In an embodiment, the propagation characteristicincludes a multipath interference characteristic.

In an embodiment, the path analysis engine 3152 is configured to test acharacteristic or parameter of the at least two power transmissionpathways 3180. In an embodiment, the path analysis engine is configuredto test a line of sight transmission pathway between the sub-Nyquistholographic aperture 3130 and the target device 3190. In an embodiment,the path analysis engine is configured to test a transmission pathwaybetween the sub-Nyquist holographic aperture and the target device thatincludes a reflection off a radiofrequency electromagnetic wavereflecting surface. For example, a reflection pathway may help avoid thehuman being 3198. In an embodiment, the path analysis engine isconfigured to test a multipath transmission pathway between thesub-Nyquist holographic aperture and the target device. In anembodiment, a first transmission pathway of the at least two powertransmission pathways has an initial first directional orientationrelative to the surface 3124 and a second transmission pathway of the atleast two power transmission pathways has a second and different initialdirectional orientation relative to the surface from the firstdirectional orientation. In an embodiment, the radiateable space 3102includes a free space radiateable by the antenna 3110.

In an embodiment, the path analysis engine 3152 is further configured torespectively test the at least two power transmission pathways 3180using a channel sounding technique. In an embodiment, the path analysisengine is further configured to respectively test a respectivepropagation characteristic of the at least two power transmissionpathways using a channel sounding technique. In an embodiment, the pathanalysis engine is further configured to respectively test a respectivepropagation characteristic or parameter of the at least two powertransmission pathways using a channel sounding technique. In anembodiment, the path analysis engine includes a path analysis engineconfigured to evaluate or simulate at least two power transmissionpathways from the antenna 3110 to the target device 3190 located withinthe radiateable space 3102.

In an embodiment, the optimization circuit 3154 is configured to selecta best available wireless power transmission regime from at least twoavailable wireless power transmission regimes. In an embodiment, theoptimization circuit is configured to select a wireless powertransmission regime maximizing a wireless transfer of radiofrequencyelectromagnetic power from the antenna to a target device, the selectionconstrained by a radiofrequency electromagnetic wave radiation exposurelimit placed on a human being. In an embodiment, the maximizing includesmaximizing a density of electromagnetic power transferred from theantenna to the target device. In an embodiment, the maximizing includesmaximizing an efficiency of electromagnetic power transferred from theantenna to the target device. In an embodiment, the maximizing includesmaximizing a transfer of electromagnetic power from the antenna to thetarget device, the maximizing responsive to a set of configurable rules.In an embodiment, the optimization circuit is configured to select awireless power transmission regime that includes a multipath wirelesspower transmission regime. In an embodiment, the optimization circuit isconfigured to select a wireless power transmission regime that includesa reflection off a surface power transmission pathway. For example, thereflection may be a specular or a diffuse reflection. In an embodiment,the optimization circuit is configured to select a wireless powertransmission regime that includes a line of sight power transmissionpathway. In an embodiment, the wireless power transmission regimeincludes a wireless power transmission regime facilitating a wirelesstransfer of electromagnetic power in the radiative far-field region. Inan embodiment, the wireless power transmission regime includes awireless power transmission regime facilitating a wireless transfer ofelectromagnetic power in the radiative near-field. In an embodiment, thewireless power transmission regime includes a wireless powertransmission regime facilitating a wireless transfer of electromagneticpower in the reactive near-field.

In an embodiment, the optimization circuit 3154 is configured to selecta wireless power transmission regime in response to a matrixfactorization, or a matrix decomposition based optimization technique.In an embodiment, the optimization circuit is configured to select awireless power transmission regime in response to a gradient descentbased optimization technique. For example, the gradient descent basedoptimization technique may include a local maximization optimization, orglobal maximization optimization technique. In an embodiment, theoptimization circuit is configured to select a wireless powertransmission regime in response to a singular value decomposition basedoptimization technique. In an embodiment, the optimization circuit isconfigured to select a wireless power transmission regime in response toa principle component analysis based optimization technique. In anembodiment, the optimization circuit is configured to select a wirelesspower transmission regime optimized utilizing coherent superposition ofradiofrequency electromagnetic waves transmitted by the antenna. In anembodiment, the optimization circuit is configured to select a wirelesspower transmission regime in response to a trial and error, or a bruteforce based optimization technique. In an embodiment, the optimizationcircuit includes a graphics processing unit.

In an embodiment, the gain definition circuit 3154 is configured to aselect a best available complex radiofrequency electromagnetic fieldfrom the at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields implementing the selected wireless powertransmission regime. In an embodiment, the gain definition circuit isconfigured to select a complex radiofrequency electromagnetic fieldconfigured to wirelessly transfer a focused electromagnetic power in theradiative far-field from the at least two selectable, arbitrary complexradiofrequency electromagnetic fields. In an embodiment, the selectedarbitrary complex radiofrequency electromagnetic field is configured toform a focused electromagnetic power beam. In an embodiment, the gaindefinition circuit is configured to select a complex radiofrequencyelectromagnetic field configured to wirelessly transfer a focusedelectromagnetic power in the radiative near-field from the at least twoselectable, arbitrary complex radiofrequency electromagnetic fields. Inan embodiment, the selected arbitrary complex radiofrequencyelectromagnetic field is configured to form a focused electromagneticpower beam. In an embodiment, the selected arbitrary complexradiofrequency electromagnetic field is configured to form aquasi-Gaussian electromagnetic beam having a radiative near-fielddistribution. In an embodiment, the selected arbitrary complexradiofrequency electromagnetic field is configured to produce a focusedtransversely localized complex radiofrequency electromagnetic field. Forexample, the transversely localized may include in a directiontransverse to a line of sight between the surface and the target device.In an embodiment, the focused transversely localized complexradiofrequency electromagnetic field is formed by a coherentsuperposition of at least two electromagnetic fields. For example, thefocused transversely localized complex radiofrequency electromagneticfield may be determined in response to Green's function or thefundamental solution technique. In an embodiment, the selected arbitrarycomplex radiofrequency electromagnetic field is configured to form afocused electromagnetic power beam and a focused transversely localizedcomplex radiofrequency electromagnetic field. In an embodiment, the gaindefinition circuit is configured to select a complex radiofrequencyelectromagnetic field configured to wirelessly transfer focusedelectromagnetic power in the reactive near-field from the at least twoselectable, arbitrary complex radiofrequency electromagnetic fields. Inan embodiment, the selected arbitrary complex radiofrequencyelectromagnetic field is configured to produce a focused transverselylocalized complex radiofrequency electromagnetic field. In anembodiment, the focused transversely localized complex radiofrequencyelectromagnetic field is formed by a coherent superposition of at leasttwo electromagnetic fields. In an embodiment, the gain definitioncircuit is configured to select a complex radiofrequency electromagneticfield best implementing the selected wireless power transmission regimefrom the at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields.

In an embodiment, the gain definition circuit 3154 is configured todetermine a matrix representation of a transfer function responsive tothe selected wireless power transmission regime. The gain definitioncircuit is also configured to select a complex electromagnetic fieldimplementing the matrix representation of the transfer function from theat least two selectable arbitrary complex electromagnetic fields. Forexample, the matrix representation may be responsive to an amplitude orphase requirement. For example, the matrix representation may representan adjustment pattern. For example, the transfer function may be a totaltransfer function. For example, the selected arbitrary complexelectromagnetic field may include a selected arbitrary complexelectromagnetic field representing the holographic transfer function. Inan embodiment, the gain definition circuit is configured to determine amatrix representation of a transfer function calculated to produce theselected wireless power transmission regime. In an embodiment, the gaindefinition circuit 3154 is configured to determine a holographictransmission function responsive to the selected wireless powertransmission regime. For example, a holographic transmission functionmay be described as a holographic transfer function. The gain definitioncircuit is also configured to select a complex electromagnetic fieldimplementing the holographic transmission function from the at least twoselectable arbitrary complex electromagnetic fields. For example, thegain definition circuit may be configured to selected a complexelectromagnetic field best implementing the holographic transmissionfunction from the at least two selectable arbitrary complexelectromagnetic fields. In an embodiment, the gain definition circuit isconfigured to determine a holographic transmission function calculatedto produce the selected wireless power transmission regime. In anembodiment, the gain definition circuit is configured to determineholographic transmission function providing an antenna radiation patterndescriptive of the selected wireless power transmission regime. In anembodiment, the gain definition circuit is configured to determine anamplitude-and-phase-controlled holographic transmission functionresponsive to the selected wireless power transmission regime. The gaindefinition circuit is also configured to select a complexelectromagnetic field implementing the amplitude-and-phase-controlledholographic transmission function from the at least two selectablearbitrary complex electromagnetic fields. For example, the gaindefinition circuit may be configured to select a complex electromagneticfield best implementing the amplitude-and-phase-controlled holographictransmission function. In an embodiment, the gain definition circuit isconfigured to determine an amplitude-and-phase-controlled holographictransmission function responsive to the selected wireless powertransmission regime and responsive to a presence of the target device ina reactive near-field of the antenna.

The following description includes an example of how a holographictransmission function may be calculated or estimated. Beginning firstwith an amplitude-controlled (scalar) transmission hologram, suppose onewants to create a monochromatic, stationary field distributionE_(o)(x,y) on an (x,y) plane. The function E_(o)(x,y) is complex-valued.The field is generated by an illumination function E_(ref) (x,y). Inthis example, the stationary field distribution E_(o) may be illustratedby the transmitted radiofrequency electromagnetic wave 1942 and theillumination function E_(ref) represented by incident radiofrequencyelectromagnetic wave 1940 of FIG. 3. In a holographic design method, thetransmission function is taken proportional to the positive, real-valuedexpression |E_(o)(x,y)+E_(ref)(x,y)|², so that the transmission function

T(x,y)=b|E _(o)(x,y)+E _(ref)(x,y)|² =bE _(o)(x,y)E _(ref)*(x,y)+ . . .,  (1)

where b is a coefficient of proportionality chosen such that T does notexceed unity. When this transmission coefficient is applied to theillumination function, the transmitted fieldE_(T)(x,y)=T(x,y)E_(ref)(x,y) is produced. This field consists of fourterms, one of which corresponds to the first term in the r.h.s. of (1):

E _(T1)(x,y)=bE _(o)(x,y)|E _(ref)(x,y)|².  (2)

This term is directly proportional to the complex-valued amplitudeE_(o)(x,y). If the reference field further has the form

E _(ref)(x,y)=Ae ^(i(K) ^(x) ^(x+K) ^(y) ^(y)),  (3)

the field E_(T1)(x,y) reproduces the desired field E_(o)(x,y) preciselywith both its amplitude and phase, up to an overall constant coefficientof proportionality. The plane-wave-like reference field of the form (3)could be produced by an obliquely incident plane wave, or by radiationleaking from a planar waveguide, in which case {right arrow over(K)}=(K_(x),K_(y)) is the wave vector of a propagating mode in thatwaveguide. For the following, we assume that the wavenumber inside thewaveguide exceeds the free space wavenumber, k₀. This, among otherthings, ensures that the waveguide modes are fully confined(non-radiating), even if one of its walls is partially transparent to EMradiation.

When a hologram is generated by an amplitude-controlled metamaterialaperture, the full generated field is different from the desired fieldE_(o)(x,y) due to the terms neglected in the expansion of the r.h.s. of(1). However, when the illumination field is generated by a waveguide,this difference exists only in the reactive near-field zone, defined asthe region of existence of the evanescent fields. The other three terms,which were neglected in the r.h.s of (1), correspond to non-propagating,evanescent fields. It is easy to understand that from the followingexample. Assume that the desired field E_(o)(x,y) is an aperturecross-section of a propagating plane wave, i.e. E_(o)(x,y)=Ae^(i(k) ^(x)^(x+k) ^(y) ^(y)), where the wave vector k=(k_(x),k_(y)) is shorter thanthe free space wavenumber, k₀. Then, all four terms in Eq. (1) arecertain plane waves. The first one is a plane wave with transverse wavevector (k_(x),k_(y)), same as the desired object field. This is apropagating plane wave. The second term,E_(o)*(x,y)E_(ref)(x,y)E_(ref)(x,y), is a plane wave with transversewave vector 2{right arrow over (K)}−{right arrow over (k)}; this wave isevanescent because its transverse wavenumber exceeds the free-spacewavenumber. Since it is evanescent, it does not essentially existoutside the reactive near-field. This is true whenever β=|{right arrowover (K)}|, the wavenumber in the waveguide, is greater than thefree-space wavenumber, and |{right arrow over (k)}| is less than k₀.Similarly, the third and the fourth terms in Eq. 1, E_(ref)(x,y)|E_(o)(x,y)|² and E_(ref)(x,y)|E_(ref)(x,y)|², are evanescent waveswith transverse wave vector {right arrow over (K)}.

For a general field distribution, one may consider E_(o)(x,y) to be asum of plane waves, each with a transverse wave number no greater thank₀. By applying the argument above, we conclude that a general (scalar)field distribution absent of evanescent waves can be generated preciselyby an amplitude-controlled transmission hologram. A vector fielddistribution is generated similarly using a superposition ofpolarization-selective transmission holograms and a polarization-diversesource field.

In an amplitude- and phase-controlled transmission hologram, one maychoose the transfer function to be a complex-valued function of the form

T(x,y)=bE _(o)(x,y)E _(ref)*(x,y),  (1′)

that is, the transmission function that produces only the exact termgiven by Eq. 2. Phase control therefore introduces the extra degrees offreedom that can be used for a more accurate field-forming in thereactive near field. Outside of the reactive near-field, i.e. in theradiative near-field and the far field, amplitude-only holographicmethod is self-sufficient, provided that the spatial sampling of thetransmission function (1) is sufficiently high (at least higher thanNyquist sampling,

$\left. {a = {\frac{\lambda_{0}}{2} = {\pi/k_{0}}}} \right).$

In an embodiment, the gain definition circuit 3154 is configured toselect a complex electromagnetic field from the at least two selectablearbitrary complex electromagnetic fields defined in advance. In anembodiment, the gain definition circuit is configured to select acomplex electromagnetic field from the at least two selectable arbitrarycomplex electromagnetic fields defined on the fly. In an embodiment, thegain definition circuit is configured to select a complexelectromagnetic field from the at least two selectable arbitrary complexelectromagnetic fields defined based on trial and error. In anembodiment, the gain definition circuit is configured to select acomplex electromagnetic field from the at least two selectable arbitrarycomplex electromagnetic fields from a library of potential complexelectromagnetic fields.

In an embodiment, the gain definition circuit 3154 includes an adaptivegain definition circuit configured to select a second complexelectromagnetic field of the at least two complex electromagnetic field.The selection of the second complex electromagnetic field is responsiveto electromagnetic radiation received by the target device 3190 andelectromagnetic radiation received by the human being 3198 with theantenna configured in a first complex electromagnetic field of the atleast two complex electromagnetic fields. In an embodiment, the adaptivegain definition circuit is configured to select the second complexelectromagnetic field by modifying a previously implemented firstcomplex electromagnetic field. In an embodiment, the adaptive gaindefinition circuit is configured to select the at least two complexelectromagnetic fields from a library of at least three complexelectromagnetic fields.

In an embodiment, the antenna controller 3156 is configured toelectronically define the selected arbitrary complex electromagneticfield 3134 in the sub-Nyquist holographic aperture 3130. In anembodiment, the antenna controller is configured to control atransmission mode and reception mode by the antenna. In an embodiment,the antenna controller is configured to control transmission andreception by the antenna in a duplex mode. In an embodiment, the antennacontroller is configured to control transmission and reception by theantenna in a simultaneous mode.

In an embodiment, the system 3105 includes a channel sounder 3158configured to acquire data responsive to a respective characteristic orparameter of the at least two power transmission pathways 3180. Forexample, the acquired data may include a measured or an estimated data.In an embodiment, the channel sounder is configured to acquire real timedata responsive to a respective characteristic or parameter of the atleast two power transmission pathways. In an embodiment, the channelsounder includes a MIMO-type channel sounder configured to acquire dataresponsive to a respective characteristic or parameter of the at leasttwo power transmission pathways. For example, see R. S. Thoma, et. al,MIMO vector channel sounder measurement for smart antenna systemevaluation (last accessed Jan. 21, 2014, athttp://www2.elo.utfsm.cl/˜ipd481/Papers%20varios/pf01wi.021.pdf.) Forexample, the channel sounder may be configured to acquire the data inreal time. In an embodiment, the MIMO-type channel sounder is configuredto channel sound at a frequency band within the operating frequency. Inan embodiment, the MIMO-type channel sounder is configured to build anumerical matrix usable by the path analysis engine in testing the atleast two power transmission pathways.

In an embodiment, the antenna 3110 is operable in a time division duplexmode to both transmit power to the target device 3190 and to acquiredata responsive to a respective characteristic or parameter of the atleast two power transmission pathways 3180 to the target device 3190 bychannel sounding. For example, the antenna radiation patterns may betime divided between power transfer and channel sounding. For example,the antenna radiation patterns may be time divided between powertransfer and other communications. In an embodiment, the time divisionsare dynamically allocated between power transfer and channel sounding.In an embodiment, the channel sounder 3158 is configured to acquire dataresponsive to a respective characteristic or parameter of the at leasttwo power transmission pathways 3180 using a frequency division duplexmode and a time division duplex mode.

In an embodiment, the antenna 3110 is operable in a frequency divisionduplex mode to both transmit power to the target device 3190 and toacquire data responsive to a respective characteristic or parameter ofthe at least two power transmission pathways 3180 to the target deviceby channel sounding. For example, separate frequency bands may beallocated for power transfer and for channel sounding. For example, ifthe operating frequency is the 60 GHz-63 GHz frequency band, the antennamay be operated using five 500 MHz sub-band for power transfer and usingone 500 MHz sub-band for channel sounding. In an embodiment, thefrequency divisions are dynamically allocated between power transfer andchannel sounding. In an embodiment, the antenna is operable in afrequency division duplex mode to both transmit power to the targetdevice and to communicate with the target device For example, if theoperating frequency is the 60 GHz-63 GHz frequency band, the antenna maybe operated using five 500 MHz sub-band for power transfer and using one500 MHz sub-band for communication between the antenna and the targetdevice. In an embodiment, the frequency divisions are dynamicallyallocated between power transfer and communication with the targetdevice. In an embodiment, the gain definition circuit 3154 is configuredto select a first arbitrary complex radiofrequency electromagnetic fieldimplementing the selected wireless power transmission regime and selecta second arbitrary complex radiofrequency electromagnetic fieldfacilitating channel sounding the environment 3102. In an embodiment,the channel sounder is configured to acquire data responsive to arespective characteristic or parameter of the at least two powertransmission pathways using an orthogonal frequency-divisionmultiplexing protocol.

In an embodiment, the path analysis engine 3152 is configured torespectively test the at least two power transmission pathways 3180 atleast partially in response to data received from the target device3190. In an embodiment, the data received from the target deviceincludes data indicative of a density of radiofrequency electromagneticradiation received by the target device. In an embodiment, the datareceived from the target device includes data indicative of a rate ofradiofrequency electromagnetic power received by the target device fromthe antenna. In an embodiment, the data received from the target deviceincludes data indicative of a signal strength received by the targetdevice in conjunction with a channel sounding.

In an embodiment, the system 3102 includes a communications module 3162configured to communicate with the target device 3190. In an embodiment,the communications module may communicate with the target device usingthe antenna 3110, or using another antenna. The communications frequencymay be the same frequency used to transmit power, or may be a differentfrequency. In an embodiment, the communications module is configured tocommunicate with at least two target devices. For example, if theoperating frequency is the 60 GHz-63 GHz frequency band, the system maytransfer radiofrequency electromagnetic power to target device 3190Ausing five 500 MHz sub-bands, and communicate with target device 3190Ausing one 500 MHz focused sub-band for feedback; and the system maycommunicate with target device 3190B using another 500 MHz sub-band inan omni direction-mode for non-line of sight communications. In anembodiment, the communications module is configured to receive acommunication from the target device requesting a power transfer. Forexample, the target device may communicate an indication that they needpower, how much power, or a preferred power reception spectrum.

In an embodiment, the path analysis engine 3152 is configured torespectively test the at least two power transmission pathways 3180 atleast partially in response to a signal transmitted by or reflected fromanother device carried by the human being 3198. In an embodiment, thepath analysis engine is further configured to respectively test the atleast two power transmission pathways at least partially in response todata indicative of a characteristic or parameter of the environmentacquired by a sensor.

In an embodiment, the system 3102 includes a locater circuit 3164configured to determine a location of the human being 3198 in theradiateable space 3102. In an embodiment, the locater circuit isconfigured to determine a location of the human being in the radiateablespace in response to a sensor acquired data. For example, the sensoracquired data may include data acquired by an infrared, ultrasoundimaging, radio frequency imaging, radar, lidar, audio, thermal, ormotion sensor. In an embodiment, the locater circuit is configured todetermine a location of the human being in the space in response to asignal reflected by the human being or transmitted by another devicephysically associated with the human being 3198. For example, the signalmay be transmitted by a cellular device carried by the human being. Inan embodiment, the optimization circuit 3154 is configured to select awireless power transmission regime responsive to (i) the tested at leasttwo power transmission pathways and (ii) the determined location of thehuman being within the space.

In an embodiment, the system 3102 includes an update manager 3166configured to initiate an update of the selected wireless powertransmission regime. In an embodiment, the update manager is configuredto continuously initiate an update of the selected wireless powertransmission regime. In an embodiment, the update manager is configuredto periodically initiate an update of the selected wireless powertransmission regime. In an embodiment, the update manager is configuredto initiate an update of the selected wireless power transmission regimein response to a schedule. In an embodiment, the update manager isconfigured to initiate an update of the selected wireless powertransmission regime in response to an event. For example, the event mayinclude a movement by target device 3190, a movement by the human being3198, or an entry of another human into the radiateable space 3102. Inan embodiment, the update manager is configured to initiate an update ofthe selected wireless power transmission regime in response to change inelectromagnetic radiation received by the target device. In anembodiment, the update manager is configured to initiate an update ofthe selected wireless power transmission regime in response to a changeof location of the human being in the environment. In an embodiment, theupdate manager is configured to initiate an update cycle by the pathanalysis engine, the optimization circuit, the gain definition circuit,and the antenna controller.

In an embodiment, the system 3102 includes a power transfer manager 3168configured to initiate, modify, or terminate a transfer ofradiofrequency electromagnetic energy from the antenna 3110 to thetarget device 3190. In an embodiment, the initiate includes initiate atransfer in response to a request originated by the target device or inresponse to a schedule. In an embodiment, the modify includes modify anongoing transfer in response to a request originated by the targetdevice. In an embodiment, the terminate includes terminate a transfer inresponse to a request originated by the target device or in response toa schedule.

FIGS. 16-17 also illustrate an alternative embodiment of the system3105. The alternative embodiment of the system includes an antenna 3110having a sub-Nyquist holographic aperture 3130 configured to define atleast two selectable, arbitrary complex radiofrequency electromagneticfields on a surface 3124 over an operating frequency. The systemincludes a path analysis engine 3152 configured to respectively test atleast two power transmission pathways from the antenna to a targetdevice 3190 located in an environment 3100 within a space 3102radiateable by the antenna. An optimization circuit 3154 is configuredto select responsive to the tested at least two power transmissionpathways a wireless power transmission regime. The selected wirelesspower transmission regime including an electromagnetic radiation patternshaped to wirelessly transfer radiofrequency electromagnetic power fromthe antenna to the target device without exceeding anywhere in the spacea radiofrequency electromagnetic wave radiation exposure limit for ahuman being 3198. The system includes a gain definition circuit 3154configured to select a complex electromagnetic field from the at leasttwo selectable arbitrary complex electromagnetic fields implementing theselected wireless power transmission regime. The system includes anantenna controller 3156 configured to define the selected arbitrarycomplex electromagnetic field 3134 in the sub-Nyquist holographicaperture.

FIG. 18 illustrates an alternative embodiment 3102A of the radiateablespace 3102 of FIG. 16. For example, the radiateable space may includeliving room, a conference room, an office, or a hotel room. In thisalternative embodiment, the antenna 3110 is incorporated in a frame orscreen of a flat screen display, such as may be used to displaytelevision programs, videos, or computer generated displays. In thisalternative embodiment, the system 3102 of FIG. 16 wirelessly detectsand transfers radiofrequency electromagnetic power to a target device3190, illustrated by target devices 3190A-3190D, while reducing orminimizing the power received by the human being 3198 or animals.

FIG. 19 illustrates an alternative embodiment 3102B of the radiateablespace 3102 of FIG. 16. For example, the radiateable space may include apublic space, such as an airport waiting area, coffee shop, or store. Inthis alternative embodiment, the antenna 3110 is incorporated in a frameor screen of a flat screen display, such as may be used to displaytelevision programs, videos, or computer generated displays. In thisalternative embodiment, the system 3102 of FIG. 16 wirelessly detectsand transfers radiofrequency electromagnetic power to a target device3190, illustrated by target devices 3190A-3190D, while reducing orminimizing the power received by the human 3198.

FIG. 20 illustrates alternative embodiments 3110A and 3110 B of theantenna 3110 illustrated in conjunction with FIGS. 18-19. In thealternative embodiment of the antenna 3110A, the sub-Nyquist holographicaperture includes the elements 1300 carried by at least one side of aframe around a flat screen display. In the alternative embodiment of theantenna 3110B, the sub-Nyquist holographic aperture includes theelements 1300 carried by or incorporated in the screen of the flatscreen display. For example, the elements may be small enough not to bereadily noticeable by the human eye, or may be fabricated by atransparent material such as a thin layer of indium tin oxide.

FIG. 21 illustrates an example operational flow 3200. After a startoperation, the operational flow includes an investigation operation3210. The investigation operation includes testing at least tworespective power transmission pathways from an antenna to a targetdevice located within a space radiateable by the antenna. In anembodiment, the investigation operation may be implemented using thepath analysis engine 3152 to test at least two respective powertransmission pathways, such as the pathways 3180A and 3180B described inconjunction with FIGS. 32 and 33. An optimization operation 3220includes selecting responsive to the tested at least two powertransmission pathways a wireless power transmission regime. The selectedwireless power transmission regime including an electromagneticradiation pattern shaped to wirelessly transfer radiofrequencyelectromagnetic power from the antenna to a target device withoutexceeding anywhere in the space a radiofrequency electromagnetic waveradiation exposure limit for a human being. In an embodiment, theoptimization operation may be implemented using the optimization circuit3154 described in conjunction with FIGS. 16 and 17. A gain selectionoperation 3230 includes selecting a complex radiofrequencyelectromagnetic field implementing the selected wireless powertransmission regime from at least two selectable arbitrary complexelectromagnetic fields. In an embodiment, the gain selection operationmay be implemented using the gain definition circuit 3154 described inconjunction with FIGS. 16 and 17. A reception operation 3240 includesreceiving radiofrequency electromagnetic waves at the surface. Areconstruction operation 3250 includes coherently reconstructing thereceived radiofrequency electromagnetic waves with the selectedarbitrary complex radiofrequency electromagnetic field defined on thesurface. In an embodiment, the reconstruction operation may beimplemented using the antenna controller circuit 3156 described inconjunction with FIGS. 16 and 17 and the sub-Nyquist holographicaperture of the antenna to define the selected arbitrary complexradiofrequency electromagnetic field. A radiation operation 3260includes wirelessly transmitting the coherently reconstructedradiofrequency electromagnetic waves to the target device. In anembodiment, the radiation operation may be implemented using the antenna3110, the sub-Nyquist holographic aperture 3130, and the selectedarbitrary complex electromagnetic field 3134 described in conjunctionwith FIGS. 16 and 17. The operational flow includes an end operation.

In an embodiment of the gain selection operation 3250, the at least twoselectable, arbitrary complex radiofrequency electromagnetic fields aredefinable on a surface of the antenna by a sub-Nyquist holographicaperture over an operating frequency. In an embodiment of the gainselection operation, the at least two selectable, arbitrary complexradiofrequency electromagnetic fields are definable on a surface andhave tangential wavenumbers up to the free-space wavenumber (k₀). In anembodiment of the gain selection operation, the at least two selectable,arbitrary complex radiofrequency electromagnetic fields are definable ona surface and have tangential wavenumbers up to 2π over the aperturespacing (k_apt=2π/a).

In an embodiment, the operational flow 3200 further includes definingthe selected arbitrary complex radiofrequency electromagnetic field onthe surface. In an embodiment, the operational flow further includescommunicating with the target device related to its radiofrequencyelectromagnetic power requirements. In an embodiment, the operationalflow further includes initiating an update of the selected wirelesspower transmission regime. In an embodiment, the operational flowincludes initiating, modifying, or terminating a transfer ofradiofrequency electromagnetic energy from the antenna to the targetdevice in response to a request originated by the target device or inresponse to a schedule.

FIG. 22 illustrates an example apparatus 3300. The apparatus includesmeans 3352 for testing at least two respective power transmissionpathways from an antenna to a target device located within a spaceradiateable by the antenna. The apparatus includes means 3354 forselecting responsive to the tested at least two power transmissionpathways a wireless power transmission regime. The wireless powertransmission regime including an electromagnetic radiation patternshaped to wirelessly transfer radiofrequency electromagnetic power fromthe antenna to a target device without exceeding a radiofrequencyelectromagnetic wave radiation exposure limit for a human being. Theapparatus includes means 3356 for selecting a complex radiofrequencyelectromagnetic field implementing the selected wireless powertransmission regime from at least two selectable, arbitrary complexradiofrequency electromagnetic fields definable on a surface of theantenna over an operating frequency. The apparatus includes means 3358for receiving radiofrequency electromagnetic waves incident to thesurface. The apparatus includes means 3362 for defining the selectedarbitrary complex radiofrequency electromagnetic field on the surface.The apparatus includes means 3364 for coherently reconstructing thereceived radiofrequency electromagnetic waves with the selectedarbitrary complex radiofrequency electromagnetic field defined on thesurface. The apparatus includes means 3366 for delivering wirelesslytransmitting the coherently reconstructed radiofrequency electromagneticwaves.

In an embodiment, the apparatus 3300 further includes means forcommunicating with the target device related to its radiofrequencyelectromagnetic power requirements. In an embodiment, the apparatusfurther includes means for initiating an update of the selected wirelesspower transmission regime. In an embodiment, the apparatus furtherincludes means initiating, modifying, or terminating a transfer ofradiofrequency electromagnetic energy from the antenna to the targetdevice in response to a request originated by the target device or inresponse to a schedule.

FIGS. 23 and 24 illustrate an embodiment. FIG. 23 illustrates certainaspects of an environment 3400. The environment includes a target device3190 and a human being 3198. In an embodiment, the environment alsoincludes things that may affect radiofrequency transmissioncharacteristics. In an embodiment, the environment includes tables,walls, window glass, floor coverings, or other absorbent or reflectivematerials. The embodiment includes the antenna 3110 and associatedsystem apparatus 3450. The antenna includes the sub-Nyquist holographicaperture 3130 configured to define at least two selectable, arbitrarycomplex radiofrequency electromagnetic fields on the surface 3124 of theantenna over an operating frequency.

FIG. 24 illustrates an embodiment of the associated system apparatus3450. The system apparatus includes a mapping engine 3452 configured tomodel the environment 3400 within a radiateable space 3402 by theantenna 3110. In an embodiment, the mapping engine is configured tomodel a location of the human being 3198. An optimization circuit 3454is configured to select responsive to the model of the environment awireless power transmission regime. The wireless power transmissionregime including an electromagnetic radiation pattern shaped towirelessly transfer radiofrequency electromagnetic power from theantenna to the target device without exceeding a radiofrequencyelectromagnetic wave radiation exposure limit for human beings. Forexample, the transmission regime may include a directionally shapedantenna gain pattern maximizing electromagnetic radiation delivered tothe target device and minimizing electromagnetic radiation delivered tothe human being. A gain definition circuit 3456 is configured to selecta complex radiofrequency electromagnetic field implementing the selectedwireless power transmission regime from the at least two selectable,arbitrary complex radiofrequency electromagnetic fields. An antennacontroller 3458 is configured to define the selected arbitrary complexelectromagnetic field 3134 in the sub-Nyquist holographic aperture 3130.

In an embodiment, the sub-Nyquist holographic aperture 3130 and thesurface 3124 are cooperatively structured so that radiofrequencyelectromagnetic waves incident upon the surface are coherentlyreconstructed by the selected arbitrary complex radiofrequencyelectromagnetic field 3134 and transmitted to the target device 3190. Inan embodiment, the sub-Nyquist holographic aperture and the surface arestructured to cooperatively transmit electromagnetic waves into freespace. The transmitted electromagnetic waves are coherentlyreconstructed by the sub-Nyquist holographic aperture from receivedincident waves and have a radiation pattern defined by the selectedarbitrary complex radiofrequency electromagnetic field. In anembodiment, the sub-Nyquist holographic aperture and the surface aresurface are structured to cooperatively transmit electromagnetic wavesinto free space, the transmitted electromagnetic waves coherentlyreflected by the sub-Nyquist holographic aperture from received incidentwaves and having a radiation pattern defined by the selected arbitrarycomplex radiofrequency electromagnetic field.

In an embodiment, the system apparatus 3450 further includes aradiofrequency electromagnetic wave generating apparatus 3476 configuredto generate and deliver radiofrequency electromagnetic waves to thesurface 3124 of the antenna 3110. The frequency of the radiofrequencyelectromagnetic waves are within at least a portion of the operatingfrequency of the antenna.

In an embodiment, the sub-Nyquist holographic aperture 3130 isconfigured to define at least two selectable, arbitrary complexradiofrequency electromagnetic fields on the surface 3124 withtangential wavenumbers up to the free-space wavenumber (k₀). In anembodiment, the sub-Nyquist holographic aperture is configured to defineat least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on a surface with tangential wavenumbers up to 2πover the aperture spacing (k_apt=2π/a).

In an embodiment, the antenna 3110 is appropriately dimensioned to beincorporated into or mounted on a consumer device. For example, theconsumer device may include a wall panel, a flat screen display (such asthe display surface described in conjunction with FIG. 1 or FIG. 2), ora wall hanging. In an embodiment, the antenna is appropriatelydimensioned to be incorporated into or mounted on a wall panel, a flatscreen display, or a wall hanging. In an embodiment, the antenna isappropriately dimensioned to be incorporated into or mounted on apicture frame or a mirror frame. In an embodiment, the antenna isappropriately dimensioned to be incorporated into or removeably mountedon a wall of a residence, hotel, office space, or public space. In anembodiment, the antenna is configured to be supported by a surface. Inan embodiment, the antenna includes an at least substantially planararrangement of at least two antenna segments. For example, the antennamay be incorporated into two segments of a frame surrounding a displaydevice, such as flat screen display. For example, the two segments mayinclude perpendicular or parallel segments of a fame surrounding thedisplay device. In an embodiment, the antenna includes a firstsubstantially planar antenna segment physically spaced apart from asecond substantially planar antenna segment. In an embodiment, theantenna controller 3458 is configured to define the selected arbitrarycomplex radiofrequency electromagnetic field using the at least twoantenna segments.

In an embodiment, the antenna 3110 includes a radiofrequencyelectromagnetic wave radiating element and an electronicallycontrollable or tunable reflective surface. For example, theelectronically controllable or tunable reflective surface may include areconfigurable electronically controllable or tunable reflectivesurface. In an embodiment, the radiating element and the reflectivesurface are physically integrated. In an embodiment, the radiatingelement and the reflective surface are physically spaced apart.

In an embodiment, the antenna 3110 includes an electronicallycontrollable or tunable lens configured to define the at least twoselectable, arbitrary complex radiofrequency electromagnetic fields on asurface of the lens. In an embodiment, the lens includes anelectronically tunable or MEMS tunable refracting or diffracting lens.In an embodiment, the lens includes an electronically tunablemetamaterial-based refracting or diffracting lens. In an embodiment, themetamaterial-based refracting or diffracting lens including at least onelayer of a plurality of individual electromagnetic wave scatteringelements electronically operable in combination to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields on asurface over an operating frequency. In an embodiment, the lens includesa metasurface lens. For example, a metasurface lens may include atwo-dimensional metamaterial pattern consisting of an array ofsubwavelength-spaced optical nanoantennas on a flat silicon surfaceproviding an aberration-free focusing lens. In an embodiment the antennacontroller 3458 is configured to define the selected arbitrary complexradiofrequency electromagnetic field in the electronically controllableor tunable lens.

In an embodiment, the target device 3190 includes a relativelystationary target device. In an embodiment, the target device includes amoving target device. In an embodiment, the target device is configuredto receive the radiofrequency electromagnetic power wirelesslytransmitted by the antenna. In an embodiment, the target device includesa target device antenna configured to receive wirelessly transmittedradiofrequency electromagnetic power. In an embodiment, the targetdevice includes at least two target devices. In an embodiment, thetarget device includes an energy storage device rechargeable at least inpart using wirelessly transmitted radiofrequency electromagnetic powerreceived from the antenna 3110. In an embodiment, the target device isoperable at least in part using wirelessly transmitted radiofrequencyelectromagnetic power received from the antenna. For example, the targetdevice may include a mobile phone, smart phone, tablet, laptop computingdevice, or remote control. In an embodiment, the target device isconfigured to consume less than an average of one watt per hour. Forexample, the target device may include a watch, smoke detector sensor,remote control, keyboard, mouse, Bluetooth device, clock, securitysensor, or cell or smart phone. For example, the target device mayinclude emergency lighting, door locks, e-ink picture frame, live wallcalendar, or reminders.

In an embodiment, the human 3198 includes a relatively stationary humanbeing. In an embodiment, the human includes a human being in motion. Inan embodiment, the human being includes at least two humans.

In an embodiment, the mapping engine 3452 is configured to two orthree-dimensionally model the environment 3400 within the space 3402radiateable by the antenna 3110. In an embodiment, the mapping engine isconfigured to periodically update the model of the environment withinthe radiateable space 3402. In an embodiment, the mapping engine isconfigured to automatically update the model of the environment withinthe radiateable space. In an embodiment, the mapping engine isconfigured to update the model of the environment at least once asecond. In an embodiment, the mapping engine is configured to update themodel of the environment at least once each five seconds. In anembodiment, the mapping engine is configured to update the model of theenvironment at least once each ten seconds. In an embodiment, themapping engine is further configured to predictively model theenvironment. In an embodiment, the predictive model includes a predictedfuture location of the target device in the environment. For example,the future location of the target device may be predictively modeledthree or five seconds ahead. In an embodiment, the predictive modelincludes a predicted future location of the human being 3198 in theenvironment. In an embodiment, the mapping engine is configured to atleast partially model the location of the target device in response to asignal transmitted by the target. In an embodiment, the mapping engineis configured to at least partially model the location of the targetdevice in response to a signal reflected by the target device. In anembodiment, the mapping engine is configured to at least partially modelthe location of the target device in response to a characteristic orparameter of the environment within the space. In an embodiment, themapping engine is configured to at least partially model the environmentin response to data generated using a channel sounding technique. In anembodiment, the model of the environment includes an electromagneticwave reflecting surface within the radiateable space. For example, theelectromagnetic wave reflecting surface may include a wall, mirror, or areflector. In an embodiment, the model of the environment includes amodel of a power transmission pathway between the antenna and the targetdevice. For example, the model may include a model of an optimal powertransmission pathway. For example, the model may be continuouslyupdated. In an embodiment, the model of the power transmission pathwayincludes a line-of-sight transmission pathway between the antenna andthe target device. In an embodiment, the model of the power transmissionpathway includes a transmission pathway reflecting off anelectromagnetic reflecting surface located within the space. In anembodiment, the model of the power transmission pathway includes amultipath power transmission pathway.

In an embodiment, the mapping engine 3452 is configured to at leastpartially model the environment 3400 in response to sensor-acquired dataindicative of a characteristic or parameter or a parameter of theenvironment. In an embodiment, the mapping engine is configured to atleast partially model the environment in response to radio-frequencyacquired data indicative of a characteristic or parameter of theenvironment. In an embodiment, the mapping engine is configured to modela location of the human being 3198 in the environment. In an embodiment,the mapping engine is configured to initiate operation of the antenna ina radar mode, acquire radar-based data indicative of a characteristic orparameter of the environment, and model the environment at leastpartially in response to the radar-based data. In an embodiment, themapping engine is configured to at least partially model the environmentin response to lidar-acquired data indicative of a characteristic orparameter of the environment. In an embodiment, the mapping engine isconfigured to at least partially model the environment in response todata integrated using a multisensor data fusion technique. In anembodiment, the mapping engine is configured to three-dimensionallymodel the environment within the space at least partially in response todata received from the target device 3180. For example, the data may bereceived by a communications module 3464.

In an embodiment, the associated system apparatus 3450 includes a pathanalysis engine 3462 is configured to respectively test the at least twopower transmission pathways 3180. In an embodiment, the path analysisengine is configured to respectively test the at least two powertransmission pathways at least partially based on sensor-acquired 3466data indicative of a characteristic or parameter of the environment3400. In an embodiment, the path analysis engine is further configuredto respectively test the at least two power transmission pathways atleast partially in response to data assembled by multi-sensor fusiontechnique or process.

In an embodiment, the gain definition circuit 3456 is configured toselect the wireless power transmission regime responsive to (i) thewireless power transmission regime or (ii) a result of the test of theat least two power transmission pathways. In an embodiment, the gaindefinition circuit is configured to determine a matrix representation ofa transfer function responsive to the wireless power transmissionregime, and to select a complex radiofrequency electromagnetic fieldimplementing the matrix representation of the transfer function from theat least two selectable arbitrary complex radiofrequency electromagneticfields. In an embodiment, the gain definition engine is configured toselect a best available complex radiofrequency electromagnetic fieldimplementing the matrix representation of the transfer function from theat least two selectable arbitrary complex radiofrequency electromagneticfields. In an embodiment, the gain definition circuit is configured todescribe according to holographic principles an antenna radiationpattern responsive to the model of the environment, and to select acomplex radiofrequency electromagnetic field implementing the describedantenna radiation pattern from the at least two selectable arbitrarycomplex radiofrequency electromagnetic fields. In an embodiment, thegain definition circuit is configured to determine a holographictransmission function calculated to produce to the wireless powertransmission regime, and to select a complex radiofrequencyelectromagnetic field implementing the holographic transmission functionfrom the at least two selectable arbitrary complex radiofrequencyelectromagnetic fields. In an embodiment, the gain definition engine isconfigured to select a best available complex radiofrequencyelectromagnetic field implementing the holographic transmission functionfrom the at least two selectable arbitrary complex radiofrequencyelectromagnetic fields.

In an embodiment, the gain definition circuit 3456 is configured toselect complex radiofrequency electromagnetic field maximizingradiofrequency electromagnetic radiation delivered to the target device3190. The selection is constrained by a radiofrequency electromagneticwave radiation exposure limit defined for human beings. For example, thelimit may include a health and safety limit defined by a governmentagency, such as OHSA or the FCC. For example, the limit may be expressedas a power density, such as mW/cm2. For example, the limit may include apeak or a sustained power density. For example, the limit may beexpressed as a maximum permissible exposure limit. For example, thelimit may be expressed as a field strength and power density limit. Forexample, the limit may be expressed as a specific absorption rate, suchas in W/kg. In an embodiment, the complex radiofrequency electromagneticfield is selected to maximize electromagnetic radiation delivered to apower receiving antenna of the target device. In an embodiment, thecomplex radiofrequency electromagnetic field is selected to maximizeelectromagnetic radiation delivered to a field of view occupied by thetarget device, the selection constrained by a radiofrequencyelectromagnetic wave radiation limit exposure limit to a field of viewoccupied by a human being.

In an embodiment, the gain definition circuit 3456 is configured toselect responsive to the wireless power transmission regime a complexradiofrequency electromagnetic field implementing the selected wirelesspower transmission regime in an antenna having at least two aperturesegments. The selected arbitrary complex radiofrequency electromagneticfield having an amplitude or phase selected to maximize the combinedelectromagnetic radiation delivered to the target device in view of aconstraint limiting the radiofrequency electromagnetic radiation limitfor human beings. In an embodiment, the gain definition circuit isconfigured to select responsive to the wireless power transmissionregime a series of at least two complex radiofrequency electromagneticfields from the at least two selectable, arbitrary complexradiofrequency electromagnetic fields definable by the antenna. Theseries of at least two radiation patterns are selected to facilitate aniterative convergence on an arbitrary complex radiofrequencyelectromagnetic field delivering a maximum electromagnetic radiation tothe target device and constrained by a radiofrequency electromagneticwave radiation exposure limit defined for human beings. In anembodiment, the series of the at least two complex radiofrequencyelectromagnetic fields is randomly selected from at least twoselectable, arbitrary complex radiofrequency electromagnetic fieldsdefinable by the antenna.

In an embodiment, the gain definition circuit 3456 includes an adaptivegain definition circuit configured to select a second complexradiofrequency electromagnetic field of the at least two selectable,arbitrary complex radiofrequency electromagnetic fields. The selectionof the second complex radiofrequency electromagnetic field is responsiveto electromagnetic radiation received by the target device 3190 andelectromagnetic radiation received by a human being 3198 with theantenna 3110 configured in a first complex radiofrequencyelectromagnetic field of the at least two selectable, arbitrary complexradiofrequency electromagnetic fields. In an embodiment, the adaptivegain definition circuit is configured to define the series of at leasttwo radiation patterns in response to a selection algorithm.

In an embodiment, the antenna controller 3458 is configured to definethe selected arbitrary complex radiofrequency electromagnetic field 3134in the sub-Nyquist holographic aperture 3130 using a portion of thesurface 3124 of the antenna 3110. For example, the antenna controller isconfigured to use less than the antenna's entire physical aperture.

In an embodiment, the associated system apparatus 3450 includes at leastone device 3466 configured to detect or measure a characteristic orparameter of the environment 3400. In an embodiment, the at least onedevice includes an infrared sensor or a near infrared sensor. In anembodiment, the sensor includes an ultrasound sensor. In an embodiment,the at least one device includes an image acquisition device. Forexample, the image acquisition device may acquire still or streamingimages. In an embodiment, the at least one device includes a lidarimager. In an embodiment, the at least one device includes an audiosensor. In an embodiment, the at least one device includes a radiofrequency imager. In an embodiment, the radio frequency imager isconfigured to transmit or receive radio frequency electromagnetic wavesusing the antenna or another antenna. In an embodiment, the at least onedevice includes a thermal sensor. In an embodiment, the sensor includesan image sensor. For example, the image sensor may include a videotracking device, such as a Kinect device. In an embodiment, the at leastone device includes an electro-optical/infrared system. For example, anelectro-optical/infrared system may include a low resolutionelectro-optical/infrared system. For example, anelectro-optical/infrared system may include a non-imaging or imagingelectro-optical/infrared system. In an embodiment, the sensor includes amotion sensor.

In an embodiment, the associated system apparatus 3450 includes amultisensor data fusion circuit 3474 configured to receive dataindicative of a characteristic or parameter of the environment from atleast two sensors and to generate an estimate of a characteristic orparameter of the environment. For example, the data fusion circuit mayinclude a neural network. In an embodiment, the multisensor data fusioncircuit includes multisensor data fusion system employing a Bayesianfilter or a Kalman filter.

In an embodiment, the associated system apparatus 3450 includes a powertransfer manager 3472 configured to initiate, modify, or terminate atransfer of radiofrequency electromagnetic energy from the antenna 3110to the target device 3190.

In an embodiment, the associated system apparatus 3450 includes thecommunications module 3464 configured to communicate with the targetdevice. In an embodiment, the associated system apparatus includes anupdate manager 3466 configured to initiate an update of the selectedwireless power transmission regime.

FIG. 25 illustrates an example operational flow 3500. After a startoperation, the operational flow includes a simulation operation 3510.The simulation operation includes modeling an environment within a spaceradiateable by an antenna. The environment includes a target device anda human being. In an embodiment, the simulation operation may beimplemented using the mapping engine 3452 described in conjunction withFIG. 24. An optimization operation 3520 selecting responsive to themodel of the environment a wireless power transmission regime, thewireless power transmission regime including an electromagneticradiation pattern shaped to wirelessly transfer radiofrequencyelectromagnetic power from the antenna to the target device withoutexceeding a radiofrequency electromagnetic wave radiation exposure limitfor human beings. In an embodiment, the optimization operation may beimplemented using the optimization circuit 3454 described in conjunctionwith FIG. 24. A gain selection operation 3530 includes selecting acomplex radiofrequency electromagnetic field implementing the selectedwireless power transmission regime from at least two selectable,arbitrary complex radiofrequency electromagnetic fields definable on asurface of the antenna over an operating frequency. In an embodiment,the gain selection operation may be implemented using the gaindefinition circuit described in conjunction with FIG. 24. A receptionoperation 3540 includes receiving radiofrequency electromagnetic waves.A reconstruction operation 3560 includes coherently reconstructing thereceived radiofrequency electromagnetic waves with the selectedarbitrary complex radiofrequency electromagnetic field defined on thesurface. In an embodiment, the reconstruction operation may beimplemented using the antenna controller 3458 described in conjunctionwith FIG. 24 to cause the sub-Nyquist holographic aperture of theantenna to define the selected arbitrary complex radiofrequencyelectromagnetic field on the surface. A radiation operation 3560includes wirelessly transmitting radiofrequency electromagnetic power tothe target device in accordance with the identified wireless powertransmission regime. In an embodiment, the radiation operation may beimplemented using the antenna 3110, the sub-Nyquist holographic aperture3130, and the selected arbitrary complex electromagnetic field 3134described in conjunction with FIGS. 23 and 24. The operational flowincludes an end operation.

In an embodiment of the operational flow 3500, the at least twoselectable, arbitrary complex radiofrequency electromagnetic fields aredefinable on a surface of the antenna by a sub-Nyquist holographicaperture over an operating frequency. In an embodiment, the at least twoselectable, arbitrary complex radiofrequency electromagnetic fieldsdefinable on a surface have tangential wavenumbers up to the free-spacewavenumber (k₀). In an embodiment, the at least two selectable,arbitrary complex radiofrequency electromagnetic fields definable on asurface have tangential wavenumbers up to 2π over the aperture spacing(k_apt=2π/a).

In an embodiment, the operational flow 3500 further includes definingthe selected arbitrary complex radiofrequency electromagnetic field onthe surface. In an embodiment of the simulation operation 3510, themodeling includes iteratively updating the modeling of the environmentwithin a space radiateable by the antenna. In an embodiment, theoperational flow 3500 further includes testing the respective at leasttwo power transmission pathways at least partially in response tosensor-acquired data indicative of a characteristic or parameter of theenvironment. In an embodiment, the operational flow further includesacquiring data indicative of a characteristic or parameter of theenvironment. In an embodiment, the operational flow further includesgenerating an estimate of a characteristic or parameter of theenvironment by multisensor data fusion responsive to data indicative ofa characteristic or parameter of the environment respectively receivedfrom at least two sensors. In an embodiment, the operational flowfurther includes initiating an update of the selected wireless powertransmission regime. In an embodiment, the operational flow furtherincludes initiating, modifying, or terminating a transfer ofradiofrequency electromagnetic energy from the antenna to the targetdevice in response to a request originated by the target device or inresponse to a schedule.

FIG. 26 illustrates an example apparatus 3600. The apparatus includesmeans 3610 for modeling an environment within a space radiateable by anantenna, the environment including a target device and a human being.

The apparatus includes means 3520 for selecting responsive to the modelof the environment a wireless power transmission regime. The wirelesspower transmission regime including an electromagnetic radiation patternshaped to wirelessly transfer radiofrequency electromagnetic power fromthe antenna to the target device without exceeding a radiofrequencyelectromagnetic wave radiation exposure limit for human beings. Theapparatus includes means 3530 for selecting a complex radiofrequencyelectromagnetic field implementing the selected wireless powertransmission regime from at least two selectable, arbitrary complexradiofrequency electromagnetic fields definable on a surface of theantenna over an operating frequency. The apparatus includes means 3540for receiving radiofrequency electromagnetic waves. The apparatusincludes means 3550 for coherently reconstructing the receivedradiofrequency electromagnetic waves with the selected arbitrary complexradiofrequency electromagnetic field defined on the surface. Theapparatus includes means 3560 for wirelessly transmitting the coherentlyreconstructed radiofrequency electromagnetic waves to the target device.

In an embodiment, the apparatus 3600 includes means for testing therespectively at least two power transmission pathways at least partiallyin response to data indicative of a characteristic or parameter of theenvironment acquired by a sensor. In an embodiment, the apparatusincludes means for acquiring data indicative of a characteristic orparameter of the environment. In an embodiment, the apparatus includesmeans for defining the selected arbitrary complex radiofrequencyelectromagnetic field on the surface.

In an embodiment, the apparatus includes means for initiating an updateof the selected arbitrary complex electromagnetic field from the atleast two selectable arbitrary complex electromagnetic fieldsimplementing identified wireless power transmission regime. In anembodiment, the apparatus includes means for initiating, modifying, orterminating a transfer of radiofrequency electromagnetic energy from theantenna to the target device in response to a request originated by thetarget device or in response to a schedule.

FIGS. 16-20 and FIGS. 23-24 illustrate an additional embodiment. Forexample, the system 3105 includes an antenna 3110 comprising asub-Nyquist holographic aperture 3130 configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields on asurface 3124 of the antenna over an operating frequency. The systemincludes a path analysis engine 3152 configured to respectively test atleast two power transmission pathways from the antenna to a targetdevice 3190 located in an environment 3100 within a space 3102radiateable by the antenna. The target device includes a target deviceantenna comprising a sub-Nyquist holographic aperture configured todefine at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on a surface of the target device over theoperating frequency. The system includes a communications module 3162configured to receive data originated by the target device andindicative of a respective signal strength received for each of the atleast two power transmission pathways 3180. The system includes anoptimization circuit 3154 configured to select responsive to the testedat least two power transmission pathways a wireless power transmissionregime optimizing wireless transfer of radiofrequency electromagneticpower from the antenna to a target device. The selection is responsiveto data gathered by the path analysis engine and the data originated bythe target device. The system includes a gain definition circuit 3154configured to select a complex electromagnetic field from the at leasttwo selectable arbitrary complex electromagnetic fields implementing theselected wireless power transmission regime. The system includes anantenna controller 3156 configured to define the selected arbitrarycomplex electromagnetic field in the sub-Nyquist holographic aperture.In an embodiment, the target device includes a smart aperture configuredto define its aperture to maximize power reception and communicate withthe system to coordinate their respective apertures for optimizing ormaximizing power transfer.

The foregoing detailed description has set forth various embodiments ofthe devices and/or processes via the use of block diagrams, flowcharts,and/or examples. Insofar as such block diagrams, flowcharts, and/orexamples contain one or more functions and/or operations, it will beunderstood by those within the art that each function and/or operationwithin such block diagrams, flowcharts, or examples can be implemented,individually and/or collectively, by a wide range of hardware, software,firmware, or virtually any combination thereof.

All references cited herein are hereby incorporated by reference intheir entirety or to the extent their subject matter is not otherwiseinconsistent herewith.

In some embodiments, “configured” includes at least one of designed, setup, shaped, implemented, constructed, or adapted for at least one of aparticular purpose, application, or function.

It will be understood that, in general, terms used herein, andespecially in the appended claims, are generally intended as “open”terms. For example, the term “including” should be interpreted as“including but not limited to.” For example, the term “having” should beinterpreted as “having at least.” For example, the term “has” should beinterpreted as “having at least.” For example, the term “includes”should be interpreted as “includes but is not limited to,” etc. It willbe further understood that if a specific number of an introduced claimrecitation is intended, such an intent will be explicitly recited in theclaim, and in the absence of such recitation no such intent is present.For example, as an aid to understanding, the following appended claimsmay contain usage of introductory phrases such as “at least one” or “oneor more” to introduce claim recitations. However, the use of suchphrases should not be construed to imply that the introduction of aclaim recitation by the indefinite articles “a” or “an” limits anyparticular claim containing such introduced claim recitation toinventions containing only one such recitation, even when the same claimincludes the introductory phrases “one or more” or “at least one” andindefinite articles such as “a” or “an” (e.g., “a receiver” shouldtypically be interpreted to mean “at least one receiver”); the sameholds true for the use of definite articles used to introduce claimrecitations. In addition, even if a specific number of an introducedclaim recitation is explicitly recited, it will be recognized that suchrecitation should typically be interpreted to mean at least the recitednumber (e.g., the bare recitation of “at least two chambers,” or “aplurality of chambers,” without other modifiers, typically means atleast two chambers).

In those instances where a phrase such as “at least one of A, B, and C,”“at least one of A, B, or C,” or “an [item] selected from the groupconsisting of A, B, and C,” is used, in general such a construction isintended to be disjunctive (e.g., any of these phrases would include butnot be limited to systems that have A alone, B alone, C alone, A and Btogether, A and C together, B and C together, or A, B, and C together,and may further include more than one of A, B, or C, such as A₁, A₂, andC together, A, B₁, B₂, C₁, and C₂ together, or B₁ and B₂ together). Itwill be further understood that virtually any disjunctive word or phrasepresenting two or more alternative terms, whether in the description,claims, or drawings, should be understood to contemplate thepossibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase “A or B” will be understood toinclude the possibilities of “A” or “B” or “A and B.”

The herein described aspects depict different components containedwithin, or connected with, different other components. It is to beunderstood that such depicted architectures are merely examples, andthat in fact many other architectures can be implemented which achievethe same functionality. In a conceptual sense, any arrangement ofcomponents to achieve the same functionality is effectively “associated”such that the desired functionality is achieved. Hence, any twocomponents herein combined to achieve a particular functionality can beseen as “associated with” each other such that the desired functionalityis achieved, irrespective of architectures or intermedial components.Likewise, any two components so associated can also be viewed as being“operably connected,” or “operably coupled,” to each other to achievethe desired functionality. Any two components capable of being soassociated can also be viewed as being “operably couplable” to eachother to achieve the desired functionality. Specific examples ofoperably couplable include but are not limited to physically mateable orphysically interacting components or wirelessly interactable orwirelessly interacting components.

With respect to the appended claims the recited operations therein maygenerally be performed in any order. Also, although various operationalflows are presented in a sequence(s), it should be understood that thevarious operations may be performed in other orders than those which areillustrated, or may be performed concurrently. Examples of suchalternate orderings may include overlapping, interleaved, interrupted,reordered, incremental, preparatory, supplemental, simultaneous,reverse, or other variant orderings, unless context dictates otherwise.Use of “Start,” “End,” “Stop,” or the like blocks in the block diagramsis not intended to indicate a limitation on the beginning or end of anyoperations or functions in the diagram. Such flowcharts or diagrams maybe incorporated into other flowcharts or diagrams where additionalfunctions are performed before or after the functions shown in thediagrams of this application. Furthermore, terms like “responsive to,”“related to,” or other past-tense adjectives are generally not intendedto exclude such variants, unless context dictates otherwise.

While various aspects and embodiments have been disclosed herein, otheraspects and embodiments will be apparent to those skilled in the art.The various aspects and embodiments disclosed herein are for purposes ofillustration and are not intended to be limiting, with the true scopeand spirit being indicated by the following claims.

What is claimed is:
 1. An antenna comprising: a sub-Nyquistcomplex-holographic aperture configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields on asurface with tangential wavenumbers up to 2π over the aperture elementspacing (k_apt=2π/a).
 2. The antenna of claim 1, wherein the sub-Nyquistcomplex-holographic aperture includes a sub-Nyquist transmissioncomplex-holographic aperture.
 3. The antenna of claim 1, wherein thesub-Nyquist complex-holographic aperture includes a sub-Nyquistreflective complex-holographic aperture.
 4. The antenna of claim 1,wherein the sub-Nyquist complex-holographic aperture includes asub-Nyquist amplitude and phase modulation holographic aperture.
 5. Theantenna of claim 1, wherein the sub-Nyquist complex-holographic apertureincludes a plurality of individual electromagnetic wave scatteringelements distributed on the surface, each electromagnetic wavescattering element having a respective electronically controllableelectromagnetic response to an incident radiofrequency electromagneticwave, and the plurality of individual electromagnetic wave scatteringelements are electronically controllable in combination to define the atleast two selectable, arbitrary complex radiofrequency electromagneticfields on the surface.
 6. The antenna of claim 5, wherein the apertureelement spacing (k_apt=2π/a) includes the inverse of a center-to-centerspacing distance between at least two individual electromagneticscattering elements of the plurality of individual electromagnetic wavescattering elements.
 7. The antenna of claim 5, further comprising atleast two electromagnetic wave conducting structures respectivelycoupled to at least two individual electromagnetic wave scatteringelements of the plurality of individual electromagnetic wave scatteringelements.
 8. The antenna of claim 5, wherein the incident radiofrequencyelectromagnetic waves include an incident wave guide-propagatedelectromagnetic waves.
 9. The antenna of claim 5, wherein the incidentradiofrequency electromagnetic waves include incidentconductor-propagated electromagnetic waves.
 10. The antenna of claim 1,wherein the surface is a second surface of a generally planar structure,the planar structure including a first surface configured to receiveincident radiofrequency electromagnetic waves, the sub-Nyquist complexholographic aperture configured to coherently reconstruct the incidentradiofrequency electromagnetic waves responsive to a definition on thesecond surface of a selected one of the at least two selectable,arbitrary complex radiofrequency electromagnetic fields, and the secondsurface configured to transmit the coherent reconstruction of theincident radiofrequency electromagnetic waves.
 11. The antenna of claim10, wherein the transmitted coherent reconstruction of the incidentradiofrequency electromagnetic waves includes free space propagatingradiofrequency electromagnetic waves.
 12. The antenna of claim 10,wherein the transmitted coherent reconstruction of the incidentradiofrequency electromagnetic waves includes waveguide-propagatingradiofrequency electromagnetic waves.
 13. The antenna of claim 10,wherein the transmitted coherent reconstruction of the incidentradiofrequency electromagnetic waves includes conductor-propagatingradiofrequency electromagnetic waves.
 14. The antenna of claim 10,wherein the generally planar surface includes a generally planar surfacecurved in one or more directions.
 15. The antenna of claim 10, whereinthe generally planar surface includes a generally planar structurehaving a first surface and second surface spaced apart from andgenerally parallel to the first surface.
 16. The antenna of claim 1,wherein the sub-Nyquist complex-holographic aperture includes aplurality of individual electromagnetic wave scattering elementsdistributed on the surface, each electromagnetic wave scattering elementhaving a respective electronically controllable electromagnetic responseto an incident radiofrequency electromagnetic wave, and the plurality ofindividual electromagnetic wave scattering elements are electronicallycontrollable in combination to define the at least two selectable,arbitrary complex radiofrequency electromagnetic fields on the surface.17. The antenna of claim 16, wherein the plurality of individualelectromagnetic wave scattering elements are embedded within, locatedon, or located within an evanescent proximity of the surface.
 18. Theantenna of claim 1, wherein the sub-Nyquist complex-holographic apertureincludes a first sub-Nyquist complex-holographic aperture and a secondsub-Nyquist complex-holographic aperture configured in combination todefine at least two selectable, arbitrary complex radiofrequencyelectromagnetic fields on the surface with tangential wavenumbers up to2π over the aperture element spacing (k_apt=2π/a).
 19. The antenna ofclaim 18, wherein the first sub-Nyquist complex-holographic aperture andthe second sub-Nyquist complex-holographic aperture are configured to beencountered in series by incident radiofrequency electromagnetic waves.20. The antenna of claim 18, wherein the first sub-Nyquistcomplex-holographic aperture is further configured to control anamplitude of electromagnetic radiofrequency waves radiated in responseto an arbitrary complex radiofrequency electromagnetic field defined onthe surface, and the second sub-Nyquist complex-holographic aperture isfurther configured to control a phase of electromagnetic radiofrequencywaves radiated in response to an arbitrary complex radiofrequencyelectromagnetic field defined on the surface.
 21. The antenna of claim18, wherein the first sub-Nyquist complex-holographic aperture includesa plurality of individual electromagnetic wave scattering elementsdistributed on the surface, and the second sub-Nyquistcomplex-holographic aperture includes a plurality of liquid crystalphase control elements distributed on the surface.
 22. The antenna ofclaim 1, wherein each radiofrequency electromagnetic field respectivelydescribes a near-field radiative radiofrequency electromagneticradiation pattern.
 23. The antenna of claim 22, wherein each near-fieldradiative radiofrequency electromagnetic radiation pattern isrespectively configured to transmit radiofrequency electromagnetic powerto a target device.
 24. The antenna of claim 22, wherein each near-fieldradiative radiofrequency electromagnetic radiation pattern respectivelydescribes a quasi-Gaussian electromagnetic beam having a radiativenear-field distribution configured to transmit radiofrequencyelectromagnetic power to a target device.
 25. The antenna of claim 1,wherein each radiofrequency electromagnetic field describes a near-fieldreactive radiofrequency electromagnetic radiation pattern.
 26. Theantenna of claim 25, wherein each near-field reactive radiofrequencyelectromagnetic radiation pattern respectively describes a reactivenear-field sub-wavelength radiofrequency electromagnetic field patternhaving a predominantly magneto-inductive nature.
 27. The antenna ofclaim 25, wherein each near-field reactive radiofrequencyelectromagnetic radiation pattern is respectively configured to transferradiofrequency electromagnetic power to a target device.
 28. The antennaof claim 1, wherein the sub-Nyquist complex-holographic aperture and thesurface are configured to transmit coherent radiofrequencyelectromagnetic waves into free space, the transmitted radiofrequencyelectromagnetic waves coherently reconstructed by the sub-Nyquistcomplex-holographic aperture from received incident waves and have aradiation pattern defined by a selected one of the at least twoselectable, arbitrary complex radiofrequency electromagnetic fields. 29.A method comprising: receiving incident radiofrequency electromagneticwaves; defining a selected arbitrary complex radiofrequencyelectromagnetic field on a surface using a sub-Nyquistcomplex-holographic aperture configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields onthe surface with tangential wavenumbers up to 2π over the apertureelement spacing (k_apt=2π/a), the arbitrary complex radiofrequencyelectromagnetic field selected from at least two selectable, arbitrarycomplex radiofrequency electromagnetic fields; and transmittingradiofrequency electromagnetic waves coherently reconstructed from theincident radiofrequency electromagnetic waves by the selected arbitrarycomplex radiofrequency electromagnetic field defined on the surface. 30.The method of claim 29, wherein each electromagnetic field respectivelydescribes a radiative near-field electromagnetic radiation pattern. 31.The method of claim 29, wherein each electromagnetic field respectivelydescribes a reactive near-field electromagnetic radiation pattern. 32.The method of claim 29, wherein the sub-Nyquist complex-holographicaperture includes a metamaterial sub-Nyquist complex-holographicaperture.
 33. The method of claim 29, further comprising: selecting thearbitrary complex radiofrequency electromagnetic field from the at leasttwo selectable, arbitrary complex radiofrequency electromagnetic fields.34. The method of claim 29, further comprising: defining anotherselected arbitrary complex radiofrequency electromagnetic field on thesurface using the sub-Nyquist complex-holographic aperture, the otherarbitrary complex radiofrequency electromagnetic field selected from theat least two selectable, arbitrary complex radiofrequencyelectromagnetic fields; and transmitting additional radiofrequencyelectromagnetic waves coherently reconstructed from the incidentradiofrequency electromagnetic waves by the other selected arbitrarycomplex radiofrequency electromagnetic field defined on the surface. 35.An apparatus comprising: means for receiving incident radiofrequencyelectromagnetic waves; means for defining a selected arbitrary complexradiofrequency electromagnetic field on a surface with tangentialwavenumbers up to 2π over the aperture element spacing (k_apt=2π/a), thearbitrary complex radiofrequency electromagnetic field selected from atleast two selectable, arbitrary complex radiofrequency electromagneticfields; and means for transmitting radiofrequency electromagnetic wavescoherently reconstructed from the incident radiofrequencyelectromagnetic waves by the selected arbitrary complex radiofrequencyelectromagnetic field defined on the surface.
 36. The apparatus of claim35, further comprising: means for selecting the arbitrary complexradiofrequency electromagnetic field from the at least two selectable,arbitrary complex radiofrequency electromagnetic fields.
 37. A methodcomprising: receiving radiofrequency electromagnetic waves at a firstsurface of a generally planar structure having the first surface and asecond surface; defining a selected arbitrary complex radiofrequencyelectromagnetic field on the second surface using a sub-Nyquistcomplex-holographic aperture configured to define at least twoselectable, arbitrary complex radiofrequency electromagnetic fields onthe second surface with tangential wavenumbers up to 2π over theaperture spacing (k_apt=2π/a), the arbitrary complex radiofrequencyelectromagnetic field selected from the at least two selectable,arbitrary complex radiofrequency electromagnetic fields; andtransmitting from the second surface radiofrequency electromagneticwaves coherently reconstructed from the received radiofrequencyelectromagnetic waves by the selected arbitrary complex radiofrequencyelectromagnetic field defined on the second surface.
 38. The method ofclaim 37, further comprising: selecting the arbitrary complexradiofrequency electromagnetic field from the at least two selectable,arbitrary complex radiofrequency electromagnetic fields.